In 1969, and again in 1972, I gave an introductory course on topological groups at the University of London. The audience consisted largely of first-year postgraduate students in algebra or number theory and the course was designed to meet their needs, which I took to be a knowledge of basic facts about various general types of topological groups and enough about the Haar integral to enable them to appreciate its use in such contexts as representation theory and algebraic number theory. Some of the students had little or no background in topology and for this reason topological concepts were developed ab initio, whereas the rudiments of group theory were assumed.

After the 1969 course there was some demand from new students for copies of the notes and so it was decided to produce a duplicated set of notes of the 1972 lectures. I am extremely grateful to Robert Coates, Michael Rutter and Anthony Solomonides for all their hard work in preparing the mimeographed version on which the present notes are based. I have made a number of minor changes and amplified some passages when this seemed advisable for a wider audience. I have also added an informal section on the representation theory of compact groups which I intended to include in the course but for which there was no time. Its purpose is to illustrate one practical application of the Haar integral and to encourage further reading.