## Table of Contents 

## I. Introduction . 

A. Scope of this Overview. 

B. Outline of this Overview. 

C. Organization and Summary of this Overview. 

## II. Theory of Pairing Symmetries and of T$_{c}$ . 

A. Considerations on Pairing Symmetry 

1. Pairing Symmetry due to e-ph Interactions. 

2. Effective Repulsion in s-wave channel in jellium 

3. Pairing in ℓ ̸ = 0 channel due to incoherent particle-hole fluctuations. 

4. Exchange of Collective fluctuations. 

5. Symmetry of Pairing Interaction from Exchange of Spin-Fluctuations 

B. Effect of the Frequency Dependence of Fluctuations on Tc in s-wave and higher angular momentum pairing. 

C. Quantum-Criticality in Relation to in e-e Induced Pairing. 

D. Calculations of T$_{c}$ for the Hubbard Model. 

E. Excitonic Pairing. 

## III. Electron-Phonon Promoted T$_{c}$ . 

A. McMillan Expression for the Coupling constant. 

B. Empirical Relations in transition metal superconductivity. 

1. Maximum T$_{c}$ and General Lessons. 

## IV. Superconductivity from Fermion Interactions . 

A. Pairing in Dilute Fermions with varying Interactions realized in Cold Atoms in Optical Traps. 

B. Liquid He 3 : Pairing Symmetry, T$_{c}$ and Connection to Landau Theory. 

C. Empirical Results for pairing symmetry, T$_{c}$ and Quantum Fluctuations in Heavy Fermions. 

D. Superconductivity and Quantum-criticality in the Cuprates. 

