Topics to be covered during this first school include:
- Basic techniques of contact topology: Moser trick, Gray stability, contact Hamiltonians, neighbourhood and isotopy extension theorems.
- Legendrian and transverse knots in contact 3-manifolds: classical invariants, classification questions.
- Contact structures on 3-manifolds: Lutz-Martinet theorem on the existence of contact structures, tight vs. overtwisted, symplectic fillings.
- Surfaces in contact 3-manifolds, convex surface theory, tomography, classification of contact structures on 3-manifolds.
- Open books and other topological constructions of contact manifolds.