A Hiker's guide to K3. Aspects of N=(4,4) superconformal field theory with central charge c=6

We study the moduli space M of N=(4,4) superconformal field theories with central charge c=6. After a slight emendation of its global description we find the locations of various known models in the component of M associated to K3 surfaces. Among them are the Z2 and Z4 orbifold theories obtained from the torus component of M. Here, SO(4,4) triality is found to play a dominant role. We obtain the B-field values in direction of the exceptional divisors which arise from orbifolding. We prove T-duality for the Z2 orbifolds and use it to derive the form of M purely within conformal field theory. For the Gepner model (2)4 and some of its orbifolds we find the locations in M and prove isomorphisms to nonlinear σ models. In particular we prove that the Gepner model (2)4 has a geometric interpretation with Fermat quartic target space. (orig.)