diff --git a/core/src/lib.rs b/core/src/lib.rs
index b640c90..6482889 100644
--- a/core/src/lib.rs
+++ b/core/src/lib.rs
@@ -8,4 +8,5 @@
 
 pub mod codec;
 pub mod hash;
+pub mod map;
 pub mod rng;
diff --git a/core/src/map.rs b/core/src/map.rs
new file mode 100644
index 0000000..e6312e0
--- /dev/null
+++ b/core/src/map.rs
@@ -0,0 +1,190 @@
+//! Tile map of the shared world.
+
+use crate::codec::{DecodeError, Reader, Writer};
+
+/// Longest accepted map edge, in tiles.
+pub const MAX_MAP_SIZE: u32 = 1024;
+
+/// Tile coordinate. `x` grows to the right, `y` grows downwards.
+#[derive(Clone, Copy, Debug, PartialEq, Eq, PartialOrd, Ord)]
+pub struct Pos {
+    pub x: i32,
+    pub y: i32,
+}
+
+impl Pos {
+    pub const fn new(x: i32, y: i32) -> Self {
+        Self { x, y }
+    }
+}
+
+/// What a tile is made of.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+#[repr(u8)]
+pub enum Terrain {
+    /// Open ground that can be walked on.
+    Ground = 0,
+    /// Rock that a stone pickaxe can break.
+    SoftRock = 1,
+    /// Rock that needs a copper pickaxe.
+    HardRock = 2,
+    /// Indestructible rock at the edge of the map.
+    Bedrock = 3,
+}
+
+impl Terrain {
+    pub fn from_u8(value: u8) -> Option<Self> {
+        match value {
+            0 => Some(Terrain::Ground),
+            1 => Some(Terrain::SoftRock),
+            2 => Some(Terrain::HardRock),
+            3 => Some(Terrain::Bedrock),
+            _ => None,
+        }
+    }
+
+    pub fn is_walkable(self) -> bool {
+        matches!(self, Terrain::Ground)
+    }
+
+    /// Number of hits that break this terrain, or `None` if it cannot be dug.
+    pub fn hits_to_break(self) -> Option<u8> {
+        match self {
+            Terrain::SoftRock => Some(3),
+            Terrain::HardRock => Some(6),
+            Terrain::Ground | Terrain::Bedrock => None,
+        }
+    }
+
+    /// Lowest pickaxe tier that can dig this terrain, or `None` if it cannot
+    /// be dug.
+    pub fn required_tool_tier(self) -> Option<u8> {
+        match self {
+            Terrain::SoftRock => Some(1),
+            Terrain::HardRock => Some(2),
+            Terrain::Ground | Terrain::Bedrock => None,
+        }
+    }
+}
+
+/// One cell of the map.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub struct Tile {
+    pub terrain: Terrain,
+    /// Hits this tile has taken so far. Always below the number of hits that
+    /// break its terrain, and zero for terrain that cannot be dug.
+    pub damage: u8,
+}
+
+impl Tile {
+    pub const fn new(terrain: Terrain) -> Self {
+        Self { terrain, damage: 0 }
+    }
+}
+
+/// Rectangular grid of tiles.
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub struct Map {
+    width: u32,
+    height: u32,
+    tiles: Vec<Tile>,
+}
+
+impl Map {
+    /// Creates a map in which every tile has the given terrain.
+    ///
+    /// # Panics
+    /// Panics if an edge is zero or longer than [`MAX_MAP_SIZE`].
+    pub fn filled(width: u32, height: u32, terrain: Terrain) -> Self {
+        assert!(width > 0 && height > 0, "map must not be empty");
+        assert!(
+            width <= MAX_MAP_SIZE && height <= MAX_MAP_SIZE,
+            "map is too large"
+        );
+        let count = (width as usize) * (height as usize);
+        Self {
+            width,
+            height,
+            tiles: vec![Tile::new(terrain); count],
+        }
+    }
+
+    pub fn width(&self) -> u32 {
+        self.width
+    }
+
+    pub fn height(&self) -> u32 {
+        self.height
+    }
+
+    fn index(&self, pos: Pos) -> Option<usize> {
+        if pos.x < 0 || pos.y < 0 {
+            return None;
+        }
+        let (x, y) = (pos.x as u32, pos.y as u32);
+        if x >= self.width || y >= self.height {
+            return None;
+        }
+        Some((y as usize) * (self.width as usize) + (x as usize))
+    }
+
+    pub fn in_bounds(&self, pos: Pos) -> bool {
+        self.index(pos).is_some()
+    }
+
+    pub fn get(&self, pos: Pos) -> Option<Tile> {
+        self.index(pos).map(|index| self.tiles[index])
+    }
+
+    /// Replaces the tile at `pos`. Returns `false` if `pos` is outside the
+    /// map.
+    pub fn set(&mut self, pos: Pos, tile: Tile) -> bool {
+        match self.index(pos) {
+            Some(index) => {
+                self.tiles[index] = tile;
+                true
+            }
+            None => false,
+        }
+    }
+
+    /// All tiles, row by row: the tile at `pos` has index `y * width + x`.
+    pub fn tiles(&self) -> &[Tile] {
+        &self.tiles
+    }
+
+    pub fn encode(&self, w: &mut Writer) {
+        w.u32(self.width);
+        w.u32(self.height);
+        for tile in &self.tiles {
+            w.u8(tile.terrain as u8);
+            w.u8(tile.damage);
+        }
+    }
+
+    pub fn decode(r: &mut Reader<'_>) -> Result<Self, DecodeError> {
+        let width = r.u32()?;
+        let height = r.u32()?;
+        if width == 0 || height == 0 || width > MAX_MAP_SIZE || height > MAX_MAP_SIZE {
+            return Err(DecodeError::InvalidValue("map size"));
+        }
+        let count = (width as usize) * (height as usize);
+        if r.remaining() < count * 2 {
+            return Err(DecodeError::UnexpectedEnd);
+        }
+        let mut tiles = Vec::with_capacity(count);
+        for _ in 0..count {
+            let terrain = Terrain::from_u8(r.u8()?).ok_or(DecodeError::InvalidValue("terrain"))?;
+            let damage = r.u8()?;
+            if damage > 0 && damage >= terrain.hits_to_break().unwrap_or(0) {
+                return Err(DecodeError::InvalidValue("tile damage"));
+            }
+            tiles.push(Tile { terrain, damage });
+        }
+        Ok(Self {
+            width,
+            height,
+            tiles,
+        })
+    }
+}
diff --git a/core/tests/map.rs b/core/tests/map.rs
new file mode 100644
index 0000000..e078e6a
--- /dev/null
+++ b/core/tests/map.rs
@@ -0,0 +1,132 @@
+use grovewright_core::codec::{DecodeError, Reader, Writer};
+use grovewright_core::map::{Map, Pos, Terrain, Tile};
+
+#[test]
+fn a_filled_map_has_the_requested_size_and_terrain() {
+    let map = Map::filled(4, 3, Terrain::SoftRock);
+    assert_eq!(map.width(), 4);
+    assert_eq!(map.height(), 3);
+    assert_eq!(map.tiles().len(), 12);
+    assert_eq!(map.get(Pos::new(3, 2)), Some(Tile::new(Terrain::SoftRock)));
+}
+
+#[test]
+fn positions_outside_the_map_are_rejected() {
+    let mut map = Map::filled(4, 3, Terrain::Ground);
+    for pos in [
+        Pos::new(-1, 0),
+        Pos::new(0, -1),
+        Pos::new(4, 0),
+        Pos::new(0, 3),
+    ] {
+        assert!(!map.in_bounds(pos), "{pos:?}");
+        assert_eq!(map.get(pos), None, "{pos:?}");
+        assert!(!map.set(pos, Tile::new(Terrain::Bedrock)), "{pos:?}");
+    }
+    assert!(map.in_bounds(Pos::new(3, 2)));
+}
+
+#[test]
+fn set_changes_exactly_one_tile() {
+    let mut map = Map::filled(4, 3, Terrain::Ground);
+    assert!(map.set(Pos::new(1, 2), Tile::new(Terrain::HardRock)));
+    let hard_rock = map
+        .tiles()
+        .iter()
+        .filter(|tile| tile.terrain == Terrain::HardRock)
+        .count();
+    assert_eq!(hard_rock, 1);
+    assert_eq!(map.tiles()[2 * 4 + 1].terrain, Terrain::HardRock);
+}
+
+#[test]
+fn only_rock_can_be_dug() {
+    assert_eq!(Terrain::Ground.hits_to_break(), None);
+    assert_eq!(Terrain::Bedrock.hits_to_break(), None);
+    assert_eq!(Terrain::SoftRock.hits_to_break(), Some(3));
+    assert_eq!(Terrain::HardRock.hits_to_break(), Some(6));
+    assert_eq!(Terrain::Ground.required_tool_tier(), None);
+    assert_eq!(Terrain::Bedrock.required_tool_tier(), None);
+    assert_eq!(Terrain::SoftRock.required_tool_tier(), Some(1));
+    assert_eq!(Terrain::HardRock.required_tool_tier(), Some(2));
+}
+
+#[test]
+fn only_ground_can_be_walked_on() {
+    assert!(Terrain::Ground.is_walkable());
+    assert!(!Terrain::SoftRock.is_walkable());
+    assert!(!Terrain::HardRock.is_walkable());
+    assert!(!Terrain::Bedrock.is_walkable());
+}
+
+#[test]
+fn terrain_numbers_are_stable() {
+    for terrain in [
+        Terrain::Ground,
+        Terrain::SoftRock,
+        Terrain::HardRock,
+        Terrain::Bedrock,
+    ] {
+        assert_eq!(Terrain::from_u8(terrain as u8), Some(terrain));
+    }
+    assert_eq!(Terrain::from_u8(4), None);
+}
+
+#[test]
+fn a_map_survives_encoding() {
+    let mut map = Map::filled(5, 4, Terrain::Ground);
+    map.set(
+        Pos::new(2, 1),
+        Tile {
+            terrain: Terrain::SoftRock,
+            damage: 2,
+        },
+    );
+    let mut w = Writer::new();
+    map.encode(&mut w);
+    let bytes = w.into_bytes();
+    let mut r = Reader::new(&bytes);
+    assert_eq!(Map::decode(&mut r), Ok(map));
+    assert_eq!(r.finish(), Ok(()));
+}
+
+fn encoded_map(width: u32, height: u32, tiles: &[(u8, u8)]) -> Vec<u8> {
+    let mut w = Writer::new();
+    w.u32(width);
+    w.u32(height);
+    for (terrain, damage) in tiles {
+        w.u8(*terrain);
+        w.u8(*damage);
+    }
+    w.into_bytes()
+}
+
+#[test]
+fn decoding_rejects_impossible_maps() {
+    let cases: [(Vec<u8>, DecodeError); 6] = [
+        (
+            encoded_map(0, 4, &[]),
+            DecodeError::InvalidValue("map size"),
+        ),
+        (
+            encoded_map(2_000, 4, &[]),
+            DecodeError::InvalidValue("map size"),
+        ),
+        (
+            encoded_map(1, 1, &[(9, 0)]),
+            DecodeError::InvalidValue("terrain"),
+        ),
+        (
+            encoded_map(1, 1, &[(0, 1)]),
+            DecodeError::InvalidValue("tile damage"),
+        ),
+        (
+            encoded_map(1, 1, &[(1, 3)]),
+            DecodeError::InvalidValue("tile damage"),
+        ),
+        (encoded_map(2, 2, &[(0, 0)]), DecodeError::UnexpectedEnd),
+    ];
+    for (bytes, expected) in cases {
+        assert_eq!(Map::decode(&mut Reader::new(&bytes)), Err(expected));
+    }
+}