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 Whitehead's 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
Shelah's 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