Aspects of Supersymmetric Gauge Theory and String Theory

In the first part of this thesis we study some topics in N=1 supersymmeric gauge theory and therelation to matrix models. We review the relevantnon-perturbative techniques for computing effective superpotential, such asSeiberg-Witten curve. Then we review the proposal of Dijkgraaf andVafa that relates the glueball superpotentials to thecomputation in matrix models. We then consider a case of multi-tracesuperpotential. We perform the perturbative computation of glueballsuperpotential in this case and explain the subtlety in identifying theglueball superfield. We also use these techniques to studyphases of N=1 gauge theory with flavors. In the second part westudy topics in AdS/CFT correspondence and its plane wave limit. Wereview the plane wave geometry and BMN operators thatcorresponding to string modes. Then we study string interactions inthe case of a highly curved plane wave background, and demonstrate the agreements between calculations of string interactionamplitudes in the two dual theories. Finally we study D3-branegiant gravitons and open string attached to them. Giant gravitons arenon-perturbative objects that have very large R-charge.