Count the number of squares in the given figure.

To count all squares in a compound figure, classify every square by its size — that is, by how many of the smallest grid cells it encloses — and count each size-class separately; the total number of squares equals the sum of the counts across every distinct size, from the smallest unit square up to the single largest square formed by the whole figure.

The figure may be labelled as shown.

Listing every square of each size by its four corner labels:

Each row is a distinct, non-overlapping size-class, so summing every class once — 13 + 4 + 4 + 4 + 1 + 1 — checks out to the full count without double-counting or missing any square.

So the figure contains 27 squares in total.