ABSTRACT
In this lecture note, after a commemorative foreword which the reader interested in mathematical statements may entirely skip, we focus on some recent results obtained by several authors, and which originate in an attempt to understand some questions posed by Enriques in his book «Le Superficie Algebriche».
Notably, after describing the basic properties of irregular manifolds, and some history of these results, we shall concentrate on work of the present author concerning fibrations between irregular manifolds, generalizing early work of Castelnuovo-De Franchis, and giving topological characterizations of those fibrations.
After surveying results on surfaces and manifolds with irrational pencils, due to Beauville, Xiao, Siu and ourselves, we shall discuss some very recent and interesting progress (due to Green, Lazarsfeld and ourselves) in the direction of classification of irregular Kaehler manifolds.
Discussing results on the moduli of algebraic surfaces, especially results on moduli of irregular surfaces due to the present author and Reider, will naturally then lead to consider the theory of paracanonical systems on surfaces, introduced by Enriques and carried through by Green-Lazarsfeld and Beauville.
