Quads is a rather unusual territorial game. One player plays black, the other white. Each player has a set of square plastic tiles divided diagonally into 4 triangles, like so:
+-----+
|\ /|
| \ / |
| X |
| / \ |
|/ \|
+-----+
Each triangle can be either a block of their colour, or contain a set of parallel lines (in a neutral colour), running either towards the centre of the square, or parallel to the sides.
At the start of the game, each player places one of their pieces anywhere on the board. After that, players take turns to place a piece adjacent to a piece in play, and all adjacent edges of tiles must match. Play is complicated slightly because the sides of the board are also patterned, with lines parallel to the sides, and players must match these patterns as well as the ones on the tiles. The objective is to be the last player to play a tile.
After a few games, I can see this is a deep game, with the main objective being to wall off areas of the board so that only you can play in them, but I must confess to being somewhat at a loss at present about the best way to achieve this!