Here representations of finite groups are considered. It is shown how various new representations can be formed from old ones. Decomposition into irreducible representations is explained, including the role of Schur’s lemma. There is no way around the Haar integral and the regular representation. Characters of abelian groups are studied, leading to characters of representations. Fourier analysis is extended to non-abelian groups through the Peter-Weyl theory on orthogonality of regular functions. The group algebra is then investigated. Quadratic reciprocity is obtained from Fourier analysis. Finally, induced representations and their characters are discussed, together with reciprocity and Mackey theory.