Lie groups occupy a central position in modern differential geometry and physics, as they are very useful for describing the continuous symmetries of a space. This paper is an expository article meant to introduce the theory of Lie groups, as well as survey some results related to the Riemannian geometry of groups admitting invariant metrics. In particular, a non-standard proof of the classification of invariant metrics is presented. For those unfamiliar with tensor calculus, a section devoted to tensors on manifolds and the Lie derivative is included.

Author Bio

Michael Geis is a senior at Rutgers University majoring in mathematics and material science engineering. He plans to pursue a Ph.D. in mathematics starting in the fall of 2015. Michael is interested in geometric analysis, particularly geometric flow equations and global analysis, with an eye towards applications to material science.