The aim of the course is to study moduli problems in algebraic geometry and the construction of moduli spaces via geometric invariant theory. A moduli problem is a classification problem, where we have a class of objects we want to classify up to some equivalence relation; for example, hypersurfaces in a projective space up to the automorphisms of the projective space or vector bundles on a variety up to isomorphism. A moduli problem is formalised by a moduli functor and a moduli space is a scheme that represents this functor. Typically moduli spaces are constructed as a quotient of a parameter space by a group of equivalences. The construction of algebraic quotients, as opposed to topological quotients, is known as geometric invariant theory. In the course we will study moduli functors, algebraic groups and algebraic actions, affine quotients and projective quotients, as well as some classical moduli problems  (if there is sufficient interest and time permits, we will cover the construction of moduli spaces of vector bundles on a smooth projective curve).