The book "Representations of SL2(Fq)" offers a comprehensive study of Deligne-Lusztig theory, which aims to investigate the representations of finite reductive groups through geometric methods. In particular, it focuses on the group SL2(Fq), regarded as the smallest non-trivial example. This choice allows for a complete description of the theory while also providing the opportunity to illustrate the more complex aspects of representation theory. The work builds on Drinfeld's example from 1974 and extends it to modular representation theory. The author employs fundamental results from l-adic cohomology and conducts a precise examination of the geometric properties of the action of SL2(Fq) on the Drinfeld curve. At the end of the book, a concise overview of Deligne-Lusztig theory is provided, supplemented by references to examples discussed in the text. This book is aimed at students and researchers interested in Deligne-Lusztig theory.