Moduli Space Techniques in Algebraic Geometry and Symplectic Geometry

The following is my M.Sc. thesis on moduli space techniques in algebraic and symplectic geometry. It is divided into the following two parts: the first part is devoted to presenting moduli problems in algebraic geometry using a modern perspective, via the language of stacks and the second part is devoted to studying moduli problems from the perspective of symplectic geometry. The key motivation to the first part is to present the theorem of Keel and Mori [20] which answers the classical question of under what circumstances a quotient exists for the action of an algebraic group G acting on a scheme X. Part two of the thesis is a more elaborate description of the topics found in Chapter 8 of [28].