Presents a unified approach, from the point of view of Frobenius algebras' extensions, to diverse topics such as Jones' subfactor theory, Hopf algebras and subalgebras, the Yang-Baxter equation, and two-dimensional topological quantum field theories. Discusses applications and generalizations of Morita theory and Azumaya algebra due to Hirata and Sugano, and includes self-contained sections on Azumaya algebras and strongly separable algebras. An appendix offers a brief historical guide to the literature. Requires no background in Frobenius or Hopf algebras. Annotation copyrighted by Book News, Inc., Portland, OR