even for finite ℓ . (2) The net effect still is that T$_{c}$ goes up with increasing I except close to the ferromagnetic transition, where it swings downwards towards 0. This is due to the pile up of the fluctuation spectra to low energies for I close to I$_{c}$ . This has two deleterious effects on T$_{c}$ : it increases inelastic scattering and reduces the cut-off ω$_{c}$ . These conclusions are consistent with those from the analysis of the Eliashberg equations with a general form of pairing and self-energy kernel discussed above as well as with the Ward identities. A Gutzwiller-type variational wave-function with a Hubbard model on a lattice [3] with less than 1/2 filling gives much better account of the ground state properties of normal He 3 than does a paramagnon model. But the extensions to the excitation spectra with the same basic physics can not work, since putting the model on a lattice promotes antiferomagnetic correlations and does not lead to pairing interactions in the ℓ = 1, triplet channel. Heavy Fermion compounds show superconductivity, generally associated with an AFM quantum-critical point, (but note the interesting case of CeCu$_{2}$Si$_{2}$ under pressure, where two forms of criticality, AFM, and Mixed-Valence each seem to have an associated supercon- ducting region [66]), although the converse is not true; AFM quantum critical points in some heavy-fermion compounds are not accomapanied by superconductivity. Superconductivity always appears to be in a finite angular momentum state and is not due to electron-phonon interactions. Heavy Fermions in rare-earth and actinide compounds are the ultimate realization of the ideas of analyticity and continuity which underlie the Landau quasi-particle idea. In their fermi-liquid regime, the effective mass enhancement in several heavy-fermion compounds is 0(10 $^{3}$) and the quasi-particle renormalization residue z is O (10 − $^{3}$). This situation changes in the quantum-critical regime where the quasi-particle idea breaks down and transport and thermodynamic properties are not those of a Fermi liquid. This is a beautiful example of how z → 0 as T → 0, only logarithmically, produces completely different physical properties at low temperatures than z ≈ 10 − $^{3}$. Knowing the fermi-liquid renormalizations is not as useful to deduce parameters for su- C. Experimental results on Heavy Fermions 38