Riemann surfaces are fundamental objects  in mathematics and were introduced by Riemann in his thesis in 1851. They are 1-dimensional complex manifolds and algebraic curves. Moduli spaces of algebraic curves and Teichmuller spaces of Riemann surfaces have been extensively studied and are still actively studied. They have also motivated a lot of problems and results on higher dimensional complex manifolds and algebraic varieties.
In this course, we will start from basics and give an introduction to basic results on algebraic curves  and Riemann surfaces  such as the Riemann-Roch Theorem, the uniformization theorem, and some basic results on moduli spaces and Teichmuller spaces of Riemann surfaces.

Complex analysis, group theory

[1] R. Miranda,  Algebraic curves and Riemann surfaces. Graduate Studies in Mathematics, 5. American Mathematical Society, Providence, RI, 1995. xxii+390 pp.
[2] S. Donaldson, Riemann surfaces. Oxford Graduate Texts in Mathematics, 22. Oxford University Press, Oxford, 2011. xiv+286 pp.
[3] H. Farkas,  I. Kra, Riemann surfaces. Second edition. Graduate Texts in Mathematics, 71. Springer-Verlag, New York, 1992. xvi+363 pp.
[4] P. Griffiths, J. Harris, Principles of algebraic geometry. John Wiley & Sons, Inc., New York, 1994. xiv+813 pp.