This text covers a variety of topics in representation theory and is intended for graduate
students and more advanced researchers who are interested in the field. The book begins with
classical representation theory of finite groups over complex numbers and ends with results on
representation theory of quivers. The text includes in particular infinite-dimensional unitary
representations for abelian groups Heisenberg groups and SL(2) and representation theory of
finite-dimensional algebras. The last chapter is devoted to some applications of quivers
including Harish-Chandra modules for SL(2). Ample examples are provided and some are revisited
with a different approach when new methods are introduced leading to deeper results. Exercises
are spread throughout each chapter. Prerequisites include an advanced course in linear algebra
that covers Jordan normal forms and tensor products as well as basic results on groups and
rings.
