A representation of a group is given by an action of the group on a vector space; that is, for each element in the group, we have an isomorphism of the vector space, and their compositions are compatible with the group multiplication. In this seminar we will focus on the representation theory of finite groups, and in particular the symmetric group. Many prominent mathematicians have studied the representation theory of the symmetric group, such as Frobenius, Schur and Young. The representation theory of the symmetric group also has strong connections to combinatorics and geometry, and applications to other branches of mathematics, such as mathematical physics. Every representation is built out of irreducible representations and the main aim will be to describe these irreducible representations combinatorially using certain diagrams, called Young diagrams.