This book is a course in general topology, intended for students in the first year of the second cycle (in other words, students in their third univer- sity year). The course was taught during the first semester of the 1979-80 academic year (three hours a week of lecture, four hours a week of guided work). Topology is the study of the notions of limit and continuity and thus is, in principle, very ancient. However, we shall limit ourselves to the origins of the theory since the nineteenth century. One of the sources of topology is the effort to clarify the theory of real-valued functions of a...

This is an English edition of Dixmier's book, which is the first systematic exposition of the algebraic approach to representations of Lie groups via representations of (or modules over) the corresponding universal enveloping algebras, turned out to be so well written that even today it remains one of the main textbooks and reference books on the subject. In 1992, Dixmier was awarded the Leroy P. Steele prize for expository writing in mathematics. The Committee's citation described this as one of Dixmier's extraordinary books. Written with unique precision and elegance, the book provides the...