This book consists of notes based on the three introductory lecture courses given at the LMS-SERC Instructional Conference on Lie theory and algebraic groups held at Lancaster University in September 1993: Lie Algebras by Roger Carter; Lie Groups by Graeme Segal; algebraic groups by Ian Macdonald.

The aim of the course was to provide an introduction to this important area of mathematics for postgraduate students who had no previous specialised knowledge. Discussions with the students at the end of the meeting suggested that the conference had been extremely successful; it then seemed desirable to further impose on the lecturers by asking them to write-up their lectures, in order that future generations of students could also benefit from their efforts.

All three lecturers adopted the same approach of providing a crisp, fast-moving, clear introduction, while at the same time taking care to indicate more advanced material, so as to give the full flavour of the subject. It is clear, from both the lectures and the written account, that a substantial effort was made to ensure a coherent and well-harmonised presentation of these three highly interrelated themes.

The general intention of the new series of LMS-SERC Instructional Conferences is to provide postgraduate students with the opportunity to learn important mainstream core mathematics, which they might not otherwise meet.