  We discuss the quantization of the Green-Schwarz string action on $AdS_5
\times S^5$. We construct consistent, globally well-defined, gauge fixing
choices for kappa symmetry and worldsheet diffeomorphism invariance. We then
proceed to quantize the theory in a perturbation series in the inverse radius
of curvature, in a background field expansion. We discuss vertex operators and
correlation functions, and demonstrate agreement with supergravity results in
the appropriate limit.
