Save points are at the start of each Chapter. It then saves at significant points which will become apparent as you play! We can’t say what these point are specifically, as it will give some of the game away. There’s an icon that appears in the bottom left corner every time this happens. This is done to avoid the game saving mid-puzzle, spoiling the flow of the game.
Note 1: If you quit out the game before one of these save points, then the unsaved data is lost.
Note 2: There is only one save slot, so restarting the game leads to previous save data being cancelled.