You are presented with a grid containing circles, in seemingly random positions. You fill in the lines of the grid to form an island, or galaxy around each circle. The galaxy shapes must be rotationally (or 180° or two-fold) symmetric around each circle, like the shapes shown here. They resemble little spiral galaxies, hence the name of the puzzle. When the puzzle is finished, the space is completely filled with galaxies, and every galaxy shape is symmetric. You have wrought order out of chaos!
In Japan, Galaxies puzzles are known as Tentai Show, which has an interesting double meaning. It means both “astronomical show” and “two-fold rotational symmetry”.
I have carefully ordered these puzzles so that they get significantly harder as the book numbers get higher. You’ll also find that the larger (21×21) puzzles are a great deal harder than the smaller (7×7) puzzles. I suggest you start with the smaller, easier puzzles and work your way up.