  We argue that existing methods for the perturbative computation of anomalous
dimensions and the disentanglement of mixing in N = 4 gauge theory can be
considerably simplified, systematized and extended by focusing on the theory's
dilatation operator. The efficiency of the method is first illustrated at the
one-loop level for general non-derivative scalar states. We then go on to
derive, for pure scalar states, the two-loop structure of the dilatation
operator. This allows us to obtain a host of new results. Among these are an
infinite number of previously unknown two-loop anomalous dimensions, new
subtleties concerning 't Hooft's large N expansion due to mixing effects of
degenerate single and multiple trace states, two-loop tests of various
protected operators, as well as two-loop non-planar results for two-impurity
operators in BMN gauge theory. We also put to use the recently discovered
integrable spin chain description of the planar one-loop dilatation operator
and show that the associated Yang-Baxter equation explains the existence of a
hitherto unknown planar ``axial'' symmetry between infinitely many gauge theory
states. We present evidence that this integrability can be extended to all
loops, with intriguing consequences for gauge theory, and that it leads to a
novel integrable deformation of the XXX Heisenberg spin chain. Assuming that
the integrability structure extends to more than two loops, we determine the
planar three-loop contribution to the dilatation operator.
