  This paper is an extended version of four lectures at PIMS in Vancouver given
June 27 - 30, 2016. The primary goal of these lectures was to publicize the
author's recent efforts to extend to representations of linear algebraic groups
the "theory of support varieties" which has proved successful in the study of
representations of finite group schemes. The lectures offer readers an
introduction to the subject together with "homework problems, simplify and
clarify some points in the literature, and mention some directions for future
research.
