Aim of the lecture is to give an introduction to K3 surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space. The name K3 was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire. The topics of the lecture are the following: * K3 surfaces in the Enriques-Kodaira classification. * Examples; Kummer surfaces. * Basic properties of K3 surfaces; Torelli theorem and surjectivity of the period map. * The study of automorphisms on K3 surfaces: basic facts, examples. * Symplectic automorphisms of K3 surfaces, classification, moduli spaces.