The book is based on talks given at the conference in memory of Paolo Francia, held in Genova in September 2001, and it contains invited papers dedicated to Paolo Francia. The contents cover a wide spectrum of algebraic geometry. The life and work of Paolo Francia is briefly described in the introduction, together with the list of his publications. The book contains 18 contributions, by L. Badescu and M. Schneider (Formal functions, connectivity and homogeneous spaces), L. Barbieri-Viale (On algebraic 1-motives related to Hodge cycles), A. Beauville (The Szapiro inequality for higher genus fibrations), G. Borelli (On regular surfaces of general type with pg = 2 and non-birational bicanonical map), F. Catanese and F.O. Schreyer (Canonical projections on irregular algebraic surfaces),C. Ciliberto and M. M.Lopes (On surfaces with pg =2, q=1 and non-birational bicanonical map), A. Conte, M. Marchisio and J. Murre (On unirrationality of double covers of fixed degree and large dimension), A. Corti and M. Reid (Weighted Grasmanians), T. de Fernex, L. Ein (Resolution of indeterminacy of pairs) V. Guletskii and C. Pedrini (The Chow motive and the Gedeaux surface), Y. Kawamata (Francia's flip and derived categories), K. Konno (On the quadric hull of a canonical surface) A. Langer (A note on Bogomolov's instability and Higgs sheaves), A. Lanteri and R. Mallavibarrena (Jets of antimulticanonical bundle on Del Pezzo surfaces of degree < 2), M. M. Lopes and R. Pardini (A survey on the bicanonical map of surfaces with pg = 0 and K2 >2), F. Russo (The antibirational involutions of the plane and the classifications of real Del Pezzo surfaces), V. V. Shokurov (Letters of a bi-rationalist: IV.Geometry of log flips), A. J. Sommese, J. Verschelde and Ch. Wampler (A method for tracking singular paths with application to the numerical irreducible decomposition). In addition the book contains information on the conference consisting of a list of lectures and a list of participants.