This text provides an up-to-date account of Banach and locally convex algebras with a particular emphasis on general theory, representations, and homology. In his descriptions and examples of general theory, the author remains aware of traditional trends in the field analysis while breaking from convention in his approach to "the algebra of analysis" through homological algebra. Such an approach allows Helemskii to consider topics not covered at this level in any other book, including complemented and uncomplemented ideals, projective and weak tensor products of banach algebras, Taylor's multivariable holomorphic functional calculus, the Wedderburn decomposition of Banach algebras, and the homology of Banach algebras. Graduate students and researchers in Banach algebras are sure to find this an invaluable volume.