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1. Introduction; 2. Bose-Einstein condensation and superfluidity; 3. Description of a superfluid in a dilute atomic gas; 4. Breakdown of the mean-field picture—resonance superfluids; 5. Single-channel vs. two-channel approaches; 6. Poles of the molecular propagator; 7. The equivalent single-channel theory; 8. Connection with the theory of Feshbach resonances; 9. The BCS/BEC crossover; 10. Momentum distribution in a dilute Fermi gas; 11. Imaginary-time methods for single- and two-channel BCS; 12. A mean-field description for the crossover problem; 13. Summary
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