In this thesis we explore certain limits of the AdS/CFT correspondence for
integrability. This is done by calculating the action of the dilatation operator
on operators known as restricted Schur polynomials, which are AdS/CFT
dual to D3-branes known as giant gravitons. We focus on operators in N =
4 super-Yang-Mills theory, which is dual to type IIB string theory on an
AdS5×S5 background. We find that, in various cases, this theory is integrable
in a large N non-planar limit.
