  In 2008, Aharony, Bergman, Jafferis, and Maldacena (ABJM) discovered a
three-dimensional Chern-Simons theory with N = 6 supersymmetry and conjectured
that in a certain limit, this theory is dual to type IIA string theory on
AdS4xCP3. Since then, a great deal of evidence has been accumulated which
suggests that the ABJM theory is integrable in the planar limit. Integrability
is a very useful property that allows many physical observables, such as
anomalous dimensions and scattering amplitudes, to be computed efficiently. In
the first half of this thesis, we will explain how to use integrabilty to
compute the anomalous dimensions of long, single-trace operators in the ABJM
theory. In particular, we will describe how to compute them at weak coupling
using a Bethe Ansatz, and how to compute them at strong coupling using string
theory. The latter approach involves using algebraic curve and world-sheet
techniques to compute the energies of string states dual to gauge theory
operators. In the second half of this thesis, we will discuss integrability
from the point of view of on-shell scattering amplitudes in the ABJM theory. In
particular, we will describe how to parameterize the amplitudes in terms of
supertwistors and how to relate higher-point tree-level amplitudes to
lower-point tree-level amplitudes using a recursion relation. We will also
explain how this recursion relation can be used to show that all tree-level
amplitudes of the ABJM theory are invariant under dual superconformal symmetry.
This symmetry is hidden from the point of the action and implies that the
theory has Yangian symmetry, which is a key feature of integrability. This
thesis is mainly based on the material in [101], [83], and [84].
