  In the first part of this paper we provide a short introduction to the
AdS/CFT correspondence and to holographic renormalization. We discuss how QFT
correlation functions, Ward identities and anomalies are encoded in the bulk
geometry. In the second part we develop a Hamiltonian approach to the method of
holographic renormalization, with the radial coordinate playing the role of
time. In this approach regularized correlation functions are related to
canonical momenta and the near-boundary expansions of the standard approach are
replaced by covariant expansions where the various terms are organized
according to their dilatation weight. This leads to universal expressions for
counterterms and one-point functions (in the presence of sources) that are
valid in all dimensions. The new approach combines optimally elements from all
previous methods and supersedes them in efficiency.
