  These are lecture notes that arose from a representation theory course given
by the first author to the remaining six authors in March 2004 within the
framework of the Clay Mathematics Institute Research Academy for high school
students, and its extended version given by the first author to MIT
undergraduate math students in the Fall of 2008. The notes cover a number of
standard topics in representation theory of groups, Lie algebras, and quivers,
and contain many problems and exercises. They should be accessible to students
with a strong background in linear algebra and a basic knowledge of abstract
algebra, and may be used for an undergraduate or introductory graduate course
in representation theory.
