These notes follow the course of the lectures I gave at Lancaster, but contain rather more detail than it was possible to include in seven hours' lecturing time. Even so, since any adequate account of the theory of linear algebraic groups requires a book of two to three hundred pages, it is obvious that I have had to leave a lot out. I have attempted only to convey the flavour of the subject, though I am painfully aware that the experts (who ought not to be reading this anyway) may well disagree with my choice of what to put in and what to leave out, what to prove and what not to prove.

In preparing these notes I have relied heavily on the books of Borel [B], Humphreys [H] and Springer [S], to which these notes may perhaps serve as an introduction. At the end, under Notes and References, I give references to these books for the proofs of theorems not proved in the text.

[B] A. Borel, Linear Algebraic Groups (Math. Lecture Note Series, W.A. Benjamin, Inc. New York, 1969).

[H] James E. Humphreys, Linear Algebraic Groups (Graduate Texts in Mathematics, Springer-Verlag, New York, 1975).

[S] T. A. Springer, Linear Algebraic Groups (Birkhaüser, Boston, 1981)