Random Matrices in Topological String Theory

This work has been mostly motivated by the work of Dijkgraaf and Vafa, who wrote a series of papers in the summer of 2002, where they made a connection between topological string theory and large N random matrix models on the one hand, and showed a way to calculate the effective superpotential of N = 1 supersymmetric gauge theories from topological strings on the other hand. These three subjects, topological strings, random matrices and N = 1 supersymmetric gauge theories, are by themselves vast areas where one can get lost very easily. This thesis attempts to give an idea of these areas, first separately, with always in mind that they will be connected to each other, and then continues to some specific calculations that confirm the conjecture in one way or another.