Paint some empty cells black. No square of side 2 is entirely black. No black area is rectangular. All white areas are rectangular. All white areas are diagonally adjacent. A white area may contain up to one number, and that number must be its area.
The following puzzle is intended to be instructive, so not terribly hard.
Introductory in the sense that it's very easy, not in the sense that it's this blog's first puzzle of the kind. What fun would doing things in order be?
Draw a single loop through some cells of the grid. All places where the loop crosses over itself are given, and the loop goes straight at all such intersections. Some loop corners are marked. On some of these marks the number of cells occupied by the corner is given.