Almost free modules : set theoretic models This book provides a comprehensive exposition of the use of set theoretic methods in abelian group theory module theory and homological algebra including applications to Whiteheads Problem the structure of Ext and the existence of almost free modules over non perfect rings. This second edition is completely revised and udated to include major developments in the decade since the first edition. Among these are applications to cotorsion theories and covers including a proof of the Flat Cover Conjecture as well as the use of Shelahs pcf theory to constuct almost free groups. As with the first edition the book is largely self contained and designed to be accessible to both graduate students and researchers in both algebra and logic. They will find there an introduction to powerful techniques which they may find useful in their own work