This elegantly edited landmark edition of Gert Kjærgård Pedersen’s C*-Algebras and their Automorphism Groups (1979) carefully and sensitively extends the classic work to reflect the wealth of relevant novel results revealed over the past forty years. Revered from publication for its writing clarity and extremely elegant presentation of a vast space within operator algebras, Pedersen’s monograph is notable for reviewing partially ordered vector spaces and group automorphisms in unusual detail, and by strict intention releasing the C*-algebras from the yoke of representations as Hilbert space operators. Under the editorship of Søren Eilers and Dorte Olesen, the second edition modernizes Pedersen’s work for a new generation of C*-algebraists, with voluminous new commentary, all-new indexes, annotation and terminology annexes, and a surfeit of new discussion of applications and of the author’s later work. Covers basic C*-algebra theory in a short and appealingly elegant way, with a few additions and corrections given to the editors by the original author. Expands coverage to select contemporary accomplishments in C*-algebras of direct relevance to the scope of the first edition, including aspects of K-theory and set theory. Identifies key modern literature in an updated bibliography with over 100 new entries, and greatly enhances indexing throughout. Modernizes coverage of algebraic problems in relation to the theory of unitary representations of locally compact groups. Reviews mathematical accomplishments of Gert K. Pedersen in comments and a biography.