In these lectures we provide an introduction to Lusztig's classification of the irreducible characters of a finite group of Lie type. This essentially relies on structural properties of the underlying algebraic group, which will be surveyed in the first lecture. We then go on to discuss the partition of the set of characters into series and the Jordan decomposition of characters. Finally, we address the problem of computing character values, in the framework of Lusztig's theory of character sheaves.