In this talk, we introduce the theory of K3 surfaces. We begin with some examples and briefly present the importance of K3 surfaces in the study of algebraic curves and in group theory. Regarding the latter, we talk about the relation between the sporadic Matheiu group M_23 and K3 surfaces, via groups that act symplectically on these geometric objects, and about how this could generalise to larger sporadic groups and higher dimensional K3’s.