I will review the necessary requirements for S, P and D-wave supercon-
ductivity and the conditions on Antiferromagnetic Fluctuations that deter-
mine the transitions temperature for D-wave Pairing. The recently measured
spin-
uctuation spectrum near the Antiferromagnetic quantum-critical point in
CeCu2Si2 is used to calculate Tc and the temperature dependence and the co-
ecient of resistivity to substantiate the conclusions. Similar calculations show
that the measured spin-
uctuation spectrum in the Cuprate high temperature
superconductors cannot be responsible for their superconductivity or normal
state anomalies.
The phase diagram of the Cuprates is reviewed pointing out the region of
quantum-critical
uctuations and the order necessary in under-doped Cuprates
to generate them. The theory of such an order, its quantum-critical
uctuations
and the coupling of such
uctuations to fermions to generate the normal state
anomalies and D-wave will be brie
y described. The deduction of the
uctuation
spectrum from inversion of Angle-Resolved Photoemission is also demonstrated.