  The dilatation generator measures the scaling dimensions of local operators
in a conformal field theory. In this thesis we consider the example of
maximally supersymmetric gauge theory in four dimensions and develop and extend
techniques to derive, investigate and apply the dilatation operator.
  We construct the dilatation operator by purely algebraic means: Relying on
the symmetry algebra and structural properties of Feynman diagrams we are able
to bypass involved, higher-loop field theory computations. In this way we
obtain the complete one-loop dilatation operator and the planar, three-loop
deformation in an interesting subsector. These results allow us to address the
issue of integrability within a planar four-dimensional gauge theory: We prove
that the complete dilatation generator is integrable at one-loop and present
the corresponding Bethe ansatz. We furthermore argue that integrability extends
to three-loops and beyond. Assuming that it holds indeed, we finally construct
a novel spin chain model at five-loops and propose a Bethe ansatz which might
be valid at arbitrary loop-order!
  We illustrate the use of our technology in several examples and also present
two key applications for the AdS/CFT correspondence.
