Following is a description of the topics:

1. Regular and irregular singular points of linear differential equations. Classical Stokes phenomena.
2. Nonlinear Stokes phenomena. Ecalle-Voronin moduli.
3. Phragmen-Lindelof theorem for functional cochains. Galois groups and Stokes operators.
4. Complex saddlenodes: analysis and topology.
5. Desingularization theorem for vector fields. Topological classifiacation of germs of real planar vector fields.
6. Order of topologically sufficient jet. Desingularization in the families.
7. Nonaccumulation theorem for hyperbolic polycycles.
8. Nonaccumulation theorem for elementary polycycles: ingredients of the proof.
9. Classical Riemann-Hilbert problem. Negative solution by Bolibrukh.
10. Nonlinear Riemann-Hilbert problem.
11. Hilbert-Arnold problem and smooth normal forms for local families. Kotova zoo.
12. Finite cyclicity of generic elementary polycycles.