© 2017

Introduction to the Theory of Lie Groups


  • Written in the author’s inimitable style

  • Includes full background on topological groups and group quotients

  • Contains many exercises and concrete examples

  • Requires only basic knowledge of topology and algebra


Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Roger Godement
    Pages 1-32
  3. Roger Godement
    Pages 33-60
  4. Roger Godement
    Pages 61-112
  5. Roger Godement
    Pages 113-140
  6. Roger Godement
    Pages 141-227
  7. Roger Godement
    Pages 229-283
  8. Back Matter
    Pages 285-293

About this book


This textbook covers the general theory of Lie groups. By first considering the case of linear groups (following von Neumann's method) before proceeding to the general case, the reader is naturally introduced to Lie theory.

Written by a master of the subject and influential member of the Bourbaki group, the French edition of this textbook has been used by several generations of students. This translation preserves the distinctive style and lively exposition of the original. Requiring only basics of topology and algebra, this book offers an engaging introduction to Lie groups for graduate students and a valuable resource for researchers.


Lie groups discrete groups linear groups locally compact groups MSC (2010): 22E15, 22E40, 58A40

Authors and affiliations

  1. 1.ParisFrance

About the authors

Roger Godement (October 1, 1921 - July 21, 2016) is known for his work in functional analysis, and also his expository books. He started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan. He started research into harmonic analysis on locally compact abelian groups, finding a number of major results; this work was in parallel but independent of similar investigations in the USSR and Japan. Work on the abstract theory of spherical functions published in 1952 proved very influential in subsequent work, particularly that of Harish-Chandra. The isolation of the concept of square-integrable representation is attributed to him. The Godement compactness criterion in the theory of arithmetic groups was a conjecture of his. He later worked with Jacquet on the zeta function of a simple algebra. He was an active member of the Bourbaki group in the early 1950s, and subsequently gave a number of significant Bourbaki seminars. He also took part in the Cartan seminar. He also wrote texts on abstract algebra and mathematical analysis.

Bibliographic information

  • Book Title Introduction to the Theory of Lie Groups
  • Authors Roger Godement
  • Series Title Universitext
  • Series Abbreviated Title Universitext
  • DOI
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-54373-4
  • eBook ISBN 978-3-319-54375-8
  • Series ISSN 0172-5939
  • Series E-ISSN 2191-6675
  • Edition Number 1
  • Number of Pages IX, 293
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Topological Groups, Lie Groups
  • Buy this book on publisher's site


“The book draws many very interesting connections, say to topological groups, that are rarely found in more recent books. Hence I believe it is a valuable source for material for courses on the topic.” (A. Cap, Monatshefte für Mathematik, Vol. 192 (4), August, 2020)

“This book is an educational text, in which practically all statements, which are contained in it, are proved. Therefore it is written for students, who want not only to study the theory of Lie groups and Lie algebras and to pass an examination, but to study the foundation of Lie theory for effectively using it in further scientific work.” (V. V. Gorbatsevich, zbMATH 1367.22001, 2017)