How many squares are there in the given figure ?

The figure may be labeled as shown:

The simple squares are QUYX, URVY, YVSW and XTWY, i.e. 4 in number.

The squares composed of two components each are IMYP, MJNY, YNKO and PYOL, i.e. 4 in number.

The square composed of three components each are AEYH, EBFY, YFCG and HYGD, i.e. 4 in number.

The square composed of four components is QRST, i.e. 1 in number.

The square composed of eight components is IJKL, i.e. in number.

The square composed of the twelve components is ABCD, i.e. 1 in number.

Total number of squares in the given figure $=3\times 4+1+1+1=15.$