This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, held from January 6-7, 2012, in Boston, MA, USA. The very wide range of topics represented in this volume illustrates the importance of methods and ideas originating in the theory of integrable systems to such diverse areas of mathematics as algebraic geometry, combinatorics, and probability theory. The volume offers a balanced combination of survey articles and research papers with important new results.