This is a 2-semester sequence of introductory courses in Gromov--Witten theory. The course will assume only basic knowledge of algebraic geometry and algebraic topology, and spend a few weeks building necessary tools.

The format of this class will include 2 hours of lectures and 2 hours of student seminar each week. The lecture should cover the basics of Gromov--Witten theory. However, since Gromov--Witten theory requires a lot of preparatory material, it would not be productive to teach it during the regular lectures. Instead, the students will be required to present the assigned material in turns (and preferably in English, although the language will be discussed among the participants). The potential benefits of this approach are manifold. Not only do the students learn better this way, but I also get to know them better. In the future, if the students plan to apply for graduate study, I will be able to write convincing letters for them. Furthermore, this way the lectures can move at a brisk pace while the background material will be discussed in details during the student seminars.

Possible topics for the two semester sequence include

1. Moduli of curves and maps
2. Virtual fundamental cycles
3. Equivariant cohomology/intersection theory and (Virtual) localization
4. Givental's formulation
5. Relative and logarithmic Gromov--Witten theory and degeneration formula
6. Orbifold Gromov--Witten theory
7. Quasimap theory
8. Donaldson--Thomas theory and other flavors of Gromov--Witten-like theories