Representation theory is the main bridge between abstract and linear algebra. Moreover, representations can be found in virtually any field in mathematics and can generalize many commonly used objects. In this talk, we will approach the fundamentals of the theory, with specific attention to the representations of groups. If time permits, we will clarify some notions useful for the following Friday talk by Prof. Bridson, such as finitely presented groups and ${\rm SL}(n,\mathbb{Z})$ representations.