1. Highlight “short-ranged,” “dilute,” and “low-energy” as three main features of interactions between ultracold atoms.
2. Introduce the important concept of the phase shift.
3. Introduce the $s$-wave scattering length as a universal parameter describing the low-energy interaction between ultracold atoms.
4. Discuss the relation between divergent scattering length, low-energy bound state, and jump of phase shift.
5. Discuss the relation between the scattering length and the scattering amplitude.
6. Discuss under what condition a positive scattering length describes repulsive interaction.
7. Discuss the condition when an algebraically decayed potential can be treated as a finite range one.
8. Introduce two types of zero-range single-channel potentials to capture the universal low-energy $s$-wave interaction between ultracold atoms.
9. Introduce the concept of renormalization condition and renormalizable theory.
10. Discuss how the spin rotational symmetry imposes constraints on interaction form for both alkali-metal and alkaline-earth-metal atoms.
11. Introduce Feshbach resonance as an important tool to tune scattering length.
12. Compare the two-channel Feshbach resonance with the single-channel shape resonance and compare the wide and the narrow resonances.
13. Introduce a zero-range two-channel model.
14. Introduce the confinement-induced resonance to tune interaction strength by an external potential.
15. Summarize three key conditions for a Feshbach resonance, and unify the optical Feshbach resonance, the orbital Feshbach resonance, and the confinement-induced resonance all in terms of these three conditions.
16. Introduce the Efimov effect as an important three-body effect at the vicinity of the two-body scattering resonance.
17. Highlight the symmetry aspect of the Efimov effect.
18. Discuss various connections between few-body and many-body physics.
19. Illustrate that few-body calculation can be used to determine properties of many-body systems by using high-temperature expansion as an example.
