These 18 papers, written by and for mathematicians, provide an overview of Hopf algebra theory and recent developments, particularly the influence of quantum groups. Topics covered include: the general structure of Hopf algebras; alternative proof of the existence of non-zero integrals in finite dimensional Hopf algebras; the classification of semisimple and pointed Hopf algebras this covers braided algebra, as well as a class of pointed Hopf algebras with set-theoretical solutions of the quantum Yang-Baxter equation, and a survey of inner and outer actions, and Galois theory; *-Hopf algebras; quantum groupoids and face algebras; infinitesimal Hopf algebras; dendriform algebras; entwined modules; and a generalization of crossed products. Annotation c. Book News, Inc., Portland, OR (booknews.com)