K3 surfaces are special complex surfaces which have fascinated geometers since the days of William R. Hamilton and Ernst E. Kummer in the mid eighteen hundreds. A particularly well-studied family of K3 surfaces, nowadays known as the Kummer surfaces, has indeed been introduced by Hamilton and Kummer.

In this talk, we give an introduction to K3 surfaces and to the methods by which their symmetries can be tracked. As we shall show, these methods yield a classification of all symmetries for Kummer surfaces and for a family of K3 surfaces which is next of kin to the Kummer surfaces, but less well-known.