Complex algebraic surfaces of general type with geometric genus $p_g=0$ have been studied by several authors but a complete classification is still out of reach.

In this talk I will describe the possibilities for surfaces of general type with $p_g=0$ having an involution (automorphism of order 2). Some examples will be constructed as double coverings of Enriques surfaces, which in turn are obtained as quotients of $K3$ surfaces.