This Handbook treats those parts of the theory of Boolean algebras of most interest to pure mathematicians: the set-theoretical abstract theory and applications and relationships to measure theory, topology, and logic. It is divided into two parts (published in three volumes). Part I (volume 1) is a comprehensive, self-contained introduction to the set-theoretical aspects of the theory of Boolean Algebras. It includes, in addition to a systematic introduction of basic algebra and topological ideas, recent developments such as the Balcar-Franek and Shelah-Shapirovskii results on free...