Quotients of products of curves, new surfaces with pg = 0 and their fundamental groups

We construct many new surfaces of general type with q=p_g=0 whose canonical model is the quotient of the product of two curves by the action of a finite group G, constructing in this way many new interesting fundamental groups which distinguish connected components of the moduli space of surfaces of general type. We indeed classify all such surfaces whose canonical model is singular (the smooth case was classified in an earlier work). As an important tool we prove a structure theorem giving a precise description of the fundamental group of quotients of products of curves by the action of a finite group G.