Surfaces isogenous to a product : their automorphisms and degenerations n this thesis I consider the automorphisms and stable degenerations of surfaces isogenous to a product. First I consider the action of the automorphisms on cohomology in the case where the group G is abelian. It is shown that if the irregularity of the surface is larger than 1 the action of G on the second cohomology is mostly faithful. For surfaces with irregularity 0 or 1 examples are given. Then I consider the stable degenerations of surfaces isogenous to a product and classify the possible singularities on them. As a result I show that the Q Gorenstein deformations of the degenerations with certain singuarities are unobstructed and get some connected components of the moduli space of stable surfaces.