1. Compare the difference between the two-body problem in a vacuum and on top of the Fermi sea.

2. Introduce the BCS mean-field theory and the BCS ground state wave function and its excitation.

3. Introduce the physical picture of BCS pairing.

4. Introduce the concept of contact using the BCS state as an example.

5. Discuss how the BCS state responds to the Zeeman field.

6. Discuss different pairing symmetries.

7. Discuss how the BCS-BEC crossover mean-field equation recovers features in both the BCS and the BEC limit.

8. Discuss different behaviors of the excitation spectrum in the BCS and the BEC regimes and determine superfluid critical velocity from the excitation spectrum.

9. Discuss how the superfluid transition temperature changes from the BCS regime to the BEC regime.

10. Introduce a list of experimental observations on the BCS-BEC crossover.

11. Discuss the challenging issues in studying the unitary Fermi gas.

12. Introduce the concept of holographic duality and the prediction of the $\eta/s$ bound.