  We give full details for the computation of the Kaluza--Klein mass spectrum
of Type IIB Supergravity on AdS_5 x T^{11}, with T^{11}=SU(2)xSU(2)/U(1), that
has recently lead to both stringent tests and interesting predictions on the
AdS_5/CFT_4 correspondence for N=1 SCFT's (hep-th/9905226). We exhaustively
explain how KK states arrange into SU(2,2|1) supermultiplets, and stress some
relevant features of the T^{11} manifold, such as the presence of topological
modes in the spectrum originating from the existence of non-trivial 3-cycles.
The corresponding Betti vector multiplet is responsible for the extra baryonic
symmetry in the boundary CFT. More generally, we use the simple T^{11} coset as
a laboratory to revive the technique and show the power of KK harmonic
expansion, in view of the present attempts to probe along the same lines also
M-theory compactifications and the AdS_4/CFT_3 map.
