diff --git a/gpx-rs/engine/src/engine/action.rs b/gpx-rs/engine/src/engine/action.rs
index 6f6aeb310..871275cc4 100644
--- a/gpx-rs/engine/src/engine/action.rs
+++ b/gpx-rs/engine/src/engine/action.rs
@@ -1,4 +1,4 @@
-use crate::{Command, FileId};
+use crate::{Command, FileId, Selection};
 
 /// Everything the frontend can ask the engine to do.
 ///
@@ -9,13 +9,14 @@ pub enum Action<'a> {
     Edit(Command<'a>),
     Undo,
     Redo,
+    /// Selects files, tracks, segments or waypoints (or the waypoints node of one file),
+    /// ignoring what does not exist: a selection left with nothing is empty, which deselects
+    /// everything. With `add`, the elements are added to the current selection when they can
+    /// be merged with it (see [`Selection::extend`]), otherwise they replace it.
     Select {
-        file_ids: Vec<FileId>,
+        selection: Selection,
+        add: bool,
     },
-    AddSelect {
-        file_ids: Vec<FileId>,
-    },
-    SelectAll,
     /// Moves the files to `index` among the other files, in the given order. Not undoable.
     Reorder {
         file_ids: Vec<FileId>,
diff --git a/gpx-rs/engine/src/engine/engine.rs b/gpx-rs/engine/src/engine/engine.rs
index b258924fa..6df8593e5 100644
--- a/gpx-rs/engine/src/engine/engine.rs
+++ b/gpx-rs/engine/src/engine/engine.rs
@@ -81,20 +81,18 @@ impl Engine {
             Action::Edit(command) => self.edit(command),
             Action::Undo => self.stack.undo(),
             Action::Redo => self.stack.redo(),
-            Action::Select { file_ids } => {
-                self.selection = Selection::File {
-                    file_ids: file_ids.into_iter().collect(),
-                };
-                None
-            }
-            Action::AddSelect { file_ids } => {
-                match &mut self.selection {
-                    Selection::File { file_ids: ids } => ids.extend(file_ids),
-                    selection => {
-                        *selection = Selection::File {
-                            file_ids: file_ids.into_iter().collect(),
-                        }
+            Action::Select { mut selection, add } => {
+                match self.stack.current() {
+                    Some(files) => selection.retain_existing(files),
+                    None => selection = Selection::Empty,
+                }
+                if add {
+                    // nothing to add: keep the selection
+                    if selection != Selection::Empty {
+                        self.selection.extend(selection);
                     }
+                } else {
+                    self.selection = selection;
                 }
                 None
             }
@@ -102,12 +100,6 @@ impl Engine {
                 self.order.move_files(&file_ids, index);
                 None
             }
-            Action::SelectAll => {
-                self.selection = Selection::File {
-                    file_ids: self.order.0.iter().copied().collect(),
-                };
-                None
-            }
         };
         let changed = self.diff.is_some()
             || self.selection != selection_before
@@ -156,7 +148,7 @@ impl Engine {
 
 #[cfg(test)]
 mod tests {
-    use crate::{Load, Metadata, New, NewTrack, Style};
+    use crate::{Load, Metadata, New, NewTrack, Style, TrackId, TrackSegmentId};
 
     use super::*;
 
@@ -402,12 +394,12 @@ mod tests {
         let a = engine.order()[0];
         // a new file is selected by the edit
         assert!(engine.selection_changed());
-        assert!(!engine.execute(Action::Select { file_ids: vec![a] }));
+        assert!(!select_files(&mut engine, &[a]));
         assert!(!engine.selection_changed());
-        assert!(engine.execute(Action::Select { file_ids: vec![] }));
+        assert!(select_files(&mut engine, &[]));
         assert!(engine.selection_changed());
         // undoing drops the selected file from the selection
-        engine.execute(Action::Select { file_ids: vec![a] });
+        select_files(&mut engine, &[a]);
         assert!(engine.execute(Action::Undo));
         assert!(engine.selection_changed());
         assert_eq!(engine.selection(), &Selection::Empty);
@@ -421,7 +413,7 @@ mod tests {
         engine.execute(Action::Undo);
         assert!(engine.statistics().total_distance.is_empty());
         engine.execute(Action::Redo);
-        engine.execute(Action::SelectAll);
+        select_all(&mut engine);
         assert_eq!(engine.statistics().total_distance.len(), 80);
     }
 
@@ -434,14 +426,14 @@ mod tests {
         let b = selected(&engine)[0];
         assert_eq!(selected(&engine), vec![b]);
 
-        assert!(engine.execute(Action::Select { file_ids: vec![a] }));
+        assert!(select_files(&mut engine, &[a]));
         assert_eq!(selected(&engine), vec![a]);
 
-        assert!(engine.execute(Action::AddSelect { file_ids: vec![b] }));
+        assert!(select_elements(&mut engine, files(&[b]), true));
         assert_eq!(selected(&engine).len(), 2);
 
-        engine.execute(Action::Select { file_ids: vec![] });
-        assert!(engine.execute(Action::SelectAll));
+        select_files(&mut engine, &[]);
+        assert!(select_all(&mut engine));
         assert_eq!(selected(&engine).len(), 2);
     }
 
@@ -449,8 +441,119 @@ mod tests {
     fn test_selection_does_not_create_undo_steps() {
         let mut engine = Engine::default();
         new(&mut engine, "a");
-        engine.execute(Action::SelectAll);
+        select_all(&mut engine);
         engine.execute(Action::Undo);
         assert!(engine.stack.current().is_none());
     }
+
+    fn select_elements(engine: &mut Engine, selection: Selection, add: bool) -> bool {
+        engine.execute(Action::Select { selection, add })
+    }
+
+    fn files(ids: &[FileId]) -> Selection {
+        Selection::File {
+            file_ids: ids.iter().copied().collect(),
+        }
+    }
+
+    fn select_files(engine: &mut Engine, ids: &[FileId]) -> bool {
+        select_elements(engine, files(ids), false)
+    }
+
+    fn select_all(engine: &mut Engine) -> bool {
+        let ids = engine.order().to_vec();
+        select_files(engine, &ids)
+    }
+
+    #[test]
+    fn test_select_elements() {
+        let mut engine = Engine::default();
+        load(&mut engine, "data/with_tracks_and_segments.gpx");
+        let file = engine
+            .stack
+            .current()
+            .unwrap()
+            .values()
+            .next()
+            .unwrap()
+            .clone();
+        assert!(file.trk.len() >= 2 && file.trk[0].trkseg.len() >= 2);
+        let (t0, t1) = (file.trk[0].id, file.trk[1].id);
+        let (s0, s1) = (file.trk[0].trkseg[0].id, file.trk[0].trkseg[1].id);
+
+        // tracks, then more tracks
+        let tracks = |ids: &[TrackId]| Selection::Track {
+            file_id: file.id,
+            trk_ids: ids.iter().copied().collect(),
+        };
+        assert!(select_elements(&mut engine, tracks(&[t0]), false));
+        assert_eq!(engine.selection(), &tracks(&[t0]));
+        assert!(select_elements(&mut engine, tracks(&[t1]), true));
+        assert_eq!(engine.selection(), &tracks(&[t0, t1]));
+
+        // segments of a track, added only within the same track
+        let segments = |trk_id, ids: &[TrackSegmentId]| Selection::TrackSegment {
+            file_id: file.id,
+            trk_id,
+            trkseg_ids: ids.iter().copied().collect(),
+        };
+        assert!(select_elements(&mut engine, segments(t0, &[s0]), true));
+        assert_eq!(engine.selection(), &segments(t0, &[s0]));
+        assert!(select_elements(&mut engine, segments(t0, &[s1]), true));
+        assert_eq!(engine.selection(), &segments(t0, &[s0, s1]));
+        // the statistics follow the selected segments
+        assert_eq!(
+            engine.statistics().total_distance.len(),
+            file.trk[0].trkseg[0].len() + file.trk[0].trkseg[1].len()
+        );
+
+        // the waypoints node
+        let node = Selection::Waypoints { file_id: file.id };
+        assert!(select_elements(&mut engine, node.clone(), false));
+        assert!(!select_elements(&mut engine, node.clone(), true));
+        assert_eq!(engine.selection(), &node);
+        assert!(engine.selection_changed() == false);
+
+        // unknown elements and files are ignored when adding
+        let unknown = tracks(&[TrackId::default()]);
+        assert!(!select_elements(&mut engine, unknown.clone(), true));
+        let unknown_file = Selection::Waypoints {
+            file_id: FileId::default(),
+        };
+        assert!(!select_elements(&mut engine, unknown_file.clone(), true));
+        assert!(!select_elements(&mut engine, Selection::Empty, true));
+        assert_eq!(engine.selection(), &node);
+
+        // and select nothing otherwise
+        assert!(select_elements(&mut engine, unknown, false));
+        assert_eq!(engine.selection(), &Selection::Empty);
+        select_elements(&mut engine, node, false);
+        assert!(select_elements(&mut engine, unknown_file, false));
+        assert_eq!(engine.selection(), &Selection::Empty);
+    }
+
+    #[test]
+    fn test_selected_elements_are_dropped_when_they_disappear() {
+        let mut engine = Engine::default();
+        load(&mut engine, "data/with_tracks_and_segments.gpx");
+        let file = engine
+            .stack
+            .current()
+            .unwrap()
+            .values()
+            .next()
+            .unwrap()
+            .clone();
+        let trk_id = file.trk[0].id;
+        select_elements(
+            &mut engine,
+            Selection::Track {
+                file_id: file.id,
+                trk_ids: [trk_id].into(),
+            },
+            false,
+        );
+        engine.execute(Action::Undo);
+        assert_eq!(engine.selection(), &Selection::Empty);
+    }
 }
diff --git a/gpx-rs/engine/src/engine/state/selection.rs b/gpx-rs/engine/src/engine/state/selection.rs
index 0f4d792ad..3ead2ba2b 100644
--- a/gpx-rs/engine/src/engine/state/selection.rs
+++ b/gpx-rs/engine/src/engine/state/selection.rs
@@ -28,24 +28,92 @@ pub enum Selection {
 }
 
 impl Selection {
-    /// Drops the files that do not exist anymore (e.g. after an undo).
+    /// Drops what does not exist anymore (e.g. after an undo): files, and the tracks, segments
+    /// and waypoints of the files that remain. A selection left with nothing becomes empty.
     pub fn retain_existing(&mut self, files: &StackEntry) {
-        match self {
-            Selection::Empty => {}
+        let empty = match self {
+            Selection::Empty => false,
             Selection::File { file_ids } => {
                 file_ids.retain(|id| files.contains_key(id));
-                if file_ids.is_empty() {
-                    *self = Selection::Empty;
-                }
+                file_ids.is_empty()
             }
-            Selection::Track { file_id, .. }
-            | Selection::TrackSegment { file_id, .. }
-            | Selection::Waypoints { file_id }
-            | Selection::Waypoint { file_id, .. } => {
-                if !files.contains_key(file_id) {
-                    *self = Selection::Empty;
+            Selection::Track { file_id, trk_ids } => match files.get(file_id) {
+                Some(file) => {
+                    trk_ids.retain(|id| file.trk.iter().any(|trk| trk.id == *id));
+                    trk_ids.is_empty()
                 }
+                None => true,
+            },
+            Selection::TrackSegment {
+                file_id,
+                trk_id,
+                trkseg_ids,
+            } => match files
+                .get(file_id)
+                .and_then(|file| file.trk.iter().find(|trk| trk.id == *trk_id))
+            {
+                Some(trk) => {
+                    trkseg_ids.retain(|id| trk.trkseg.iter().any(|seg| seg.id == *id));
+                    trkseg_ids.is_empty()
+                }
+                None => true,
+            },
+            Selection::Waypoints { file_id } => !files.contains_key(file_id),
+            Selection::Waypoint { file_id, wpt_ids } => match files.get(file_id) {
+                Some(file) => {
+                    wpt_ids.retain(|id| {
+                        file.wpt
+                            .iter()
+                            .flat_map(|chunk| &chunk.wpt)
+                            .any(|wpt| wpt.id == *id)
+                    });
+                    wpt_ids.is_empty()
+                }
+                None => true,
+            },
+        };
+        if empty {
+            *self = Selection::Empty;
+        }
+    }
+
+    /// Adds `other` to the selection: the elements are merged when they are of the same kind and
+    /// in the same place (same file, same track for segments), otherwise `other` replaces the
+    /// selection.
+    pub fn extend(&mut self, other: Selection) {
+        match (&mut *self, other) {
+            (Selection::File { file_ids }, Selection::File { file_ids: other }) => {
+                file_ids.extend(other)
             }
+            (
+                Selection::Track { file_id, trk_ids },
+                Selection::Track {
+                    file_id: other_file,
+                    trk_ids: other,
+                },
+            ) if *file_id == other_file => trk_ids.extend(other),
+            (
+                Selection::TrackSegment {
+                    file_id,
+                    trk_id,
+                    trkseg_ids,
+                },
+                Selection::TrackSegment {
+                    file_id: other_file,
+                    trk_id: other_trk,
+                    trkseg_ids: other,
+                },
+            ) if *file_id == other_file && *trk_id == other_trk => trkseg_ids.extend(other),
+            (Selection::Waypoints { file_id }, Selection::Waypoints { file_id: other })
+                if *file_id == other => {}
+            (
+                Selection::Waypoint { file_id, wpt_ids },
+                Selection::Waypoint {
+                    file_id: other_file,
+                    wpt_ids: other,
+                },
+            ) if *file_id == other_file => wpt_ids.extend(other),
+            (selection, other) => *selection = other,
         }
     }
 }
@@ -54,7 +122,7 @@ impl Selection {
 mod tests {
     use std::rc::Rc;
 
-    use crate::File;
+    use crate::{File, Track, TrackSegment, Waypoint, WaypointChunk};
 
     use super::*;
 
@@ -86,4 +154,102 @@ mod tests {
         selection.retain_existing(&files);
         assert!(matches!(selection, Selection::Empty));
     }
+
+    #[test]
+    fn test_retain_existing_elements() {
+        let mut file = File::default();
+        file.trk.push(Track {
+            trkseg: vec![TrackSegment::default()],
+            ..Default::default()
+        });
+        file.wpt.push(Rc::new(WaypointChunk {
+            wpt: vec![Waypoint::default()],
+            ..Default::default()
+        }));
+        let (file_id, trk_id) = (file.id, file.trk[0].id);
+        let (seg_id, wpt_id) = (file.trk[0].trkseg[0].id, file.wpt[0].wpt[0].id);
+        let mut files = StackEntry::default();
+        files.insert(file_id, Rc::new(file));
+
+        let mut selection = Selection::Track {
+            file_id,
+            trk_ids: [trk_id, TrackId::default()].into(),
+        };
+        selection.retain_existing(&files);
+        assert_eq!(
+            selection,
+            Selection::Track {
+                file_id,
+                trk_ids: [trk_id].into()
+            }
+        );
+
+        let mut selection = Selection::TrackSegment {
+            file_id,
+            trk_id,
+            trkseg_ids: [seg_id, TrackSegmentId::default()].into(),
+        };
+        selection.retain_existing(&files);
+        assert!(
+            matches!(&selection, Selection::TrackSegment { trkseg_ids, .. } if trkseg_ids.len() == 1)
+        );
+        // a segment under the wrong track
+        let mut selection = Selection::TrackSegment {
+            file_id,
+            trk_id: TrackId::default(),
+            trkseg_ids: [seg_id].into(),
+        };
+        selection.retain_existing(&files);
+        assert_eq!(selection, Selection::Empty);
+
+        let mut selection = Selection::Waypoint {
+            file_id,
+            wpt_ids: [wpt_id, WaypointId::default()].into(),
+        };
+        selection.retain_existing(&files);
+        assert!(matches!(&selection, Selection::Waypoint { wpt_ids, .. } if wpt_ids.len() == 1));
+        let mut selection = Selection::Waypoint {
+            file_id,
+            wpt_ids: [WaypointId::default()].into(),
+        };
+        selection.retain_existing(&files);
+        assert_eq!(selection, Selection::Empty);
+    }
+
+    #[test]
+    fn test_extend() {
+        let file_id = FileId::default();
+        let (a, b) = (TrackId::default(), TrackId::default());
+        let tracks = |ids: &[TrackId]| Selection::Track {
+            file_id,
+            trk_ids: ids.iter().copied().collect(),
+        };
+
+        // same kind and place: merged
+        let mut selection = tracks(&[a]);
+        selection.extend(tracks(&[b]));
+        assert_eq!(selection, tracks(&[a, b]));
+
+        // another file, or another kind: replaced
+        let mut selection = tracks(&[a]);
+        let other = Selection::Track {
+            file_id: FileId::default(),
+            trk_ids: [b].into(),
+        };
+        selection.extend(other.clone());
+        assert_eq!(selection, other);
+        selection.extend(Selection::Waypoints { file_id });
+        assert_eq!(selection, Selection::Waypoints { file_id });
+
+        // segments of another track: replaced
+        let seg = TrackSegmentId::default();
+        let segments = |trk_id| Selection::TrackSegment {
+            file_id,
+            trk_id,
+            trkseg_ids: [seg].into(),
+        };
+        let mut selection = segments(a);
+        selection.extend(segments(b));
+        assert_eq!(selection, segments(b));
+    }
 }
diff --git a/gpx-rs/wasm/src/lib.rs b/gpx-rs/wasm/src/lib.rs
index c4d261816..60f2a0766 100644
--- a/gpx-rs/wasm/src/lib.rs
+++ b/gpx-rs/wasm/src/lib.rs
@@ -66,14 +66,18 @@ fn edit(command: Command) -> bool {
 }
 
 /// Decodes concatenated 16-byte UUIDs.
-fn file_ids(bytes: &[u8]) -> Option<Vec<FileId>> {
+fn uuid_list(bytes: &[u8]) -> Option<Vec<uuid::Uuid>> {
     let (chunks, rest) = bytes.as_chunks::<16>();
-    rest.is_empty().then(|| {
-        chunks
-            .iter()
-            .map(|c| FileId(uuid::Uuid::from_bytes(*c)))
-            .collect()
-    })
+    rest.is_empty()
+        .then(|| chunks.iter().map(|c| uuid::Uuid::from_bytes(*c)).collect())
+}
+
+fn file_ids(bytes: &[u8]) -> Option<Vec<FileId>> {
+    uuid_list(bytes).map(|ids| ids.into_iter().map(FileId).collect())
+}
+
+fn parse_file_id(id: &str) -> Option<FileId> {
+    uuid::Uuid::parse_str(id).ok().map(FileId)
 }
 
 fn same_len(a: &[f64], b: &[f64], c: &[f64]) -> bool {
@@ -301,21 +305,76 @@ pub fn redo() -> bool {
 
 // Selection
 
-/// `file_ids_bytes`: concatenated 16-byte UUIDs.
+/// Selects files. `file_ids_bytes`: concatenated 16-byte UUIDs. Unknown files are ignored, and
+/// selecting nothing deselects everything. With `add`, the files are added to the selection if it
+/// already holds files.
 #[wasm_bindgen]
-pub fn select(file_ids_bytes: &[u8]) -> bool {
-    file_ids(file_ids_bytes).is_some_and(|file_ids| execute(Action::Select { file_ids }))
+pub fn select(file_ids_bytes: &[u8], add: bool) -> bool {
+    select_elements(
+        file_ids(file_ids_bytes).map(|ids| engine::Selection::File {
+            file_ids: ids.into_iter().collect(),
+        }),
+        add,
+    )
 }
 
-/// `file_ids_bytes`: concatenated 16-byte UUIDs.
-#[wasm_bindgen]
-pub fn add_select(file_ids_bytes: &[u8]) -> bool {
-    file_ids(file_ids_bytes).is_some_and(|file_ids| execute(Action::AddSelect { file_ids }))
+// The elements below cross as the id of their file (UUID string) and, like the files, as
+// concatenated 16-byte UUIDs. What does not exist is ignored. With `add`, the elements are added
+// to the selection when it holds elements of the same kind in the same place (same file, same
+// track for segments), otherwise they replace it.
+
+fn select_elements(selection: Option<engine::Selection>, add: bool) -> bool {
+    selection.is_some_and(|selection| execute(Action::Select { selection, add }))
 }
 
 #[wasm_bindgen]
-pub fn select_all() -> bool {
-    execute(Action::SelectAll)
+pub fn select_tracks(file_id: &str, track_ids_bytes: &[u8], add: bool) -> bool {
+    select_elements(
+        parse_file_id(file_id)
+            .zip(uuid_list(track_ids_bytes))
+            .map(|(file_id, ids)| engine::Selection::Track {
+                file_id,
+                trk_ids: ids.into_iter().map(engine::TrackId).collect(),
+            }),
+        add,
+    )
+}
+
+#[wasm_bindgen]
+pub fn select_segments(file_id: &str, track_id: &str, segment_ids_bytes: &[u8], add: bool) -> bool {
+    select_elements(
+        parse_file_id(file_id)
+            .zip(uuid::Uuid::parse_str(track_id).ok())
+            .zip(uuid_list(segment_ids_bytes))
+            .map(|((file_id, trk_id), ids)| engine::Selection::TrackSegment {
+                file_id,
+                trk_id: engine::TrackId(trk_id),
+                trkseg_ids: ids.into_iter().map(engine::TrackSegmentId).collect(),
+            }),
+        add,
+    )
+}
+
+/// Selects the node standing for all the waypoints of a file.
+#[wasm_bindgen]
+pub fn select_waypoint_group(file_id: &str) -> bool {
+    select_elements(
+        parse_file_id(file_id).map(|file_id| engine::Selection::Waypoints { file_id }),
+        false,
+    )
+}
+
+#[wasm_bindgen]
+pub fn select_waypoints(file_id: &str, waypoint_ids_bytes: &[u8], add: bool) -> bool {
+    select_elements(
+        parse_file_id(file_id)
+            .zip(uuid_list(waypoint_ids_bytes))
+            .map(|(file_id, ids)| engine::Selection::Waypoint {
+                file_id,
+                wpt_ids: ids.into_iter().map(engine::WaypointId).collect(),
+            }),
+        add,
+    )
 }
 
 // File order and structures
diff --git a/website/src/lib/engine.ts b/website/src/lib/engine.ts
index 074dc1bb3..5f0084929 100644
--- a/website/src/lib/engine.ts
+++ b/website/src/lib/engine.ts
@@ -154,16 +154,37 @@ class Engine {
         return this.run((w) => w.redo());
     }
 
-    select(fileIds: string[]) {
-        return this.run((w) => w.select(idsToBytes(fileIds)));
-    }
-
-    addSelect(fileIds: string[]) {
-        return this.run((w) => w.add_select(idsToBytes(fileIds)));
+    /**
+     * Selects files. With `add`, they are added to the selection if it already holds files.
+     * Selecting nothing (or only unknown files) deselects everything.
+     */
+    select(fileIds: string[], add = false) {
+        return this.run((w) => w.select(idsToBytes(fileIds), add));
     }
 
     selectAll() {
-        return this.run((w) => w.select_all());
+        return this.select(get(this._order));
+    }
+
+    // Selecting elements inside a file. With `add`, they are added to the selection when it holds
+    // elements of the same kind in the same place (same file, same track for segments),
+    // otherwise they replace it. Ids that do not exist are ignored.
+
+    selectTracks(fileId: string, trackIds: string[], add = false) {
+        return this.run((w) => w.select_tracks(fileId, idsToBytes(trackIds), add));
+    }
+
+    selectSegments(fileId: string, trackId: string, segmentIds: string[], add = false) {
+        return this.run((w) => w.select_segments(fileId, trackId, idsToBytes(segmentIds), add));
+    }
+
+    /** Selects the node standing for all the waypoints of the file. */
+    selectWaypointGroup(fileId: string) {
+        return this.run((w) => w.select_waypoint_group(fileId));
+    }
+
+    selectWaypoints(fileId: string, waypointIds: string[], add = false) {
+        return this.run((w) => w.select_waypoints(fileId, idsToBytes(waypointIds), add));
     }
 
     /** Moves the files, in the given order, to `index` among the other files. */