Lecture 1:
- Structure of rational points on curves
- Local solubility
- Descent and covering collections

Lecture 2:
- Rational points on curves of genus 0
- Finding points on curves of genus 1
- Heights on elliptic curves and generators

Lecture 3:
- Chabauty's method

Lecture 4:
- Quotients 
- Mordell-Weil sieve