Complex surfaces of general type: some recent progress

Abstract

Chapters : Old and new inequalities; Surfaces with $\chi =1$ and the bicanonical map; Surfaces with $p_g=4$; Surfaces isogeneous to a product, Beauville surfaces and the absolute Galois group;Lefschetz pencils and braid monodromies;DEF, DIFF and other equivalence relations.

58 pages, 8 figures, to appear in a Volume edited by Springer Verlag entitled "Global methods in complex geometry"