This volume expounds the general theory of Banach algebras and shows how their topology is often determined by their algebraic structures. It synthesizes work in this area from the past 20 years, including many new and unpublished results, and probes the questions of when homomorphisms and derivations from Banach algebras are automatically continuous and seeks canonical forms for these maps. Many specific classes of Banach algebras are described, including function algebras,group algebras, algebras of perators, C*-algebras, and radical Banach algebras. This is essential reading for anyone interested in Banach algebras as it interweaves algebra, functional analysis, complex analysis, set theory and logic.
