Lecture 1 (October 15: 14.30-16.00, Room 0.04) : Moduli and quotients Abstract: In this lecture we will introduce the concepts of moduli spaces and quotients in algebraic geometry. No knowledge of algebraic geometry is required; we shall begin by introducing the necessary basic definitions. We will then say what is meant by a moduli problem and relate the solution of such a problem to the construction of quotients of algebraic varieties by group actions. The second half of the lecture will be spent discussing examples of quotients. Lecture 2 (October 18: 14.30-16.00, Room 1.26): Calculation of quotients Abstract: This lecture is concerned with the construction of quotients using Mumford's method of geometric invariant theory. We will discuss affine and projective quotients and the concept of stability. Lecture 3 (October 19: 14.30-16.00, Room 0.03): Vector bundles on algebraic curves Abstract: In this lecture we will define vector bundles and describe the corresponding moduli problem. We will then indicate the solution of this problem and describe some of the geometric properties of the moduli spaces.