This text is appropriate for advanced undergraduate and beginning graduate students of Mathematics. Students from the physical and life sciences can also gain valuable knowledge about representation theory by reading this book. In this book, the representation theory of finite groups is gently introduced. The modular approach to representation theory is adopted in this text. The text is organized in such a way that it is self contained. It will be of interest to Mathematicians and individuals interested in learning about representation thoery of finite groups. The chapters are divided into sub-topics and are arranged in such a way that the flow of the material is continuous. We go from groups and homomorphisms to FG-modules right upto the character table of the dihedral group of eight elements.