  The AdS/CFT correspondence is developed from classical solutions on AdS_5
with two boundaries. The corresponding limits and the reduction of degrees of
freedom are discussed, as well as the required renormalization on the field
theory side. The Hamiltonian first-order approach towards the solution of
coupled gravitational/matter equations of motion is introduced, and the RG
interpretation is exposed. Finally we discuss a recent approach towards a
naturally vanishing cosmological constant which is based on the AdS/RG
correspondence.
