Surfaces with p_g = 0: Constructions and Moduli spaces, Burniat surfaces and deformations of automorphisms

The article is a slightly extended version of the talk, with the same title, which I gave at the Kinosaki Symposium on Algebraic Geometry in October 2011, and dealing with the classification of complex projective surfaces of general type with vanishing geometric genus, and especially with the moduli spaces of Burniat surfaces.