  We continue the analysis of hep-th/0303060 in the one-loop sector and present
the complete psu(2,2|4) dilatation operator of N=4 Super Yang-Mills theory.
This operator generates the matrix of one-loop anomalous dimensions for all
local operators in the theory. Using an oscillator representation we show how
to apply the dilatation generator to a generic state. By way of example, we
determine the planar anomalous dimensions of all operators up to and including
dimension 5.5, where we also find some evidence for integrability. Finally, we
investigate a number of subsectors of N=4 SYM in which the dilatation operator
simplifies. Among these we find the previously considered so(6) and su(2)
subsectors, a su(2|4) subsector isomorphic to the BMN matrix model at one-loop,
a u(2|3) supersymmetric subsector of nearly eighth-BPS states and, last but not
least, a non-compact sl(2) subsector whose dilatation operator lifts uniquely
to the full theory.
