This is a basic course on free boundary problems and I will try to make it accessible to people with some knowledge about harmonic functions.
1. History and basic types of free boundary problems.
2. Basic tools: Harnack inequalities and non-uniqueness.
3. Existence and optimal regularity of the solutions.
4. The regularity of free boundaries.
5. Classification of the singular sets of free boundaries.
6. The Harnack inequality approach to the regularity of free boundaries.
All are welcome