Lectures:  Exercises:  
Lecture 1, Wednesday, September 19, 2012 Definition of Riemann surfaces, first examples and properties. This lecture was presented by Dr. Simon Brain . 
Exercises from Lecture 1 psfile , pdffile  
Lecture 2, Wednesday, September 26, 2012 Meromorphic functions, elementary properties of morhisms (holomorphic maps) of Riemann surfaces. 
Exercises from Lecture 2 psfile , pdffile  
Lecture 3, Wednesday, October 3, 2012 Homotopy of curves, fundamental group, topological classification of compact Riemann surfaces, holomorphic maps between compact Riemann surfaces. 
Exercises from Lecture 3 psfile , pdffile  
Lecture 4, Wednesday, October 10, 2012 Degree of a holomorphic map between compact Riemann surfaces, divisors. 
Exercises from Lecture 4 psfile , pdffile  
Lecture 5, Wednesday, October 17, 2012 Sheaves of modules associated to divisors, RiemannRoch space and its finite dimensionality. 
Exercises from Lecture 5 psfile , pdffile  
Lecture 6, Wednesday, October 24, 2012 Holomorphic differential forms. 
Exercises from Lecture 6 psfile , pdffile  
Lecture 7, Wednesday, October 31, 2012 Examlpe session. Meromorphic differential forms. 
Exercises from Lecture 7 psfile , pdffile  
Lecture 8, Wednesday, November 7, 2012 Genus of a compact Riemann surface. The RiemannRoch formula, some examples. The RiemannHurwitz fomula. 
Exercises from Lecture 8 psfile , pdffile  
Lecture 9, Wednesday, November 14, 2012 Existence of nonconstant meromorphic functions. Coverings and universal coverings. Holomorphic maps of complex tori. 
Exercises from Lecture 9 psfile , pdffile  
Lecture 10, Wednesday, November 21, 2012 The space of complex tori as an "almost" Riemann surface. Meromorphic functions on complex tori. Correction: there was a mistake in the lecture. Please read carefully the statement of Exercise 40 and compare it with the corresponding statement from the lecture. 
Exercises from Lecture 10 psfile , pdffile  
Lecture 11, Wednesday, November 28, 2012 Field of meromorphic functions on complex tori, even and odd elliptic functions, complex tori as plane projective curves. 
Exercises from Lecture 11 psfile , pdffile  
Lecture 12, Wednesday, December 5, 2012 jinvariant. Integration of differential forms along curves, residue theorem and its inverse. 
Exercises from Lecture 12 psfile , pdffile  
Lecture 13, Wednesday, December 12, 2012 Residues of differential forms and existence of nonconstant meromorphic functions. Jacobian of a compact Riemann surface of positive genus. 
Exercises from Lecture 13 psfile , pdffile  
Lecture 14, Wednesday, December 19, 2012 AbelJacobi theorem and its first corollaries. Compact Riemann surfaces as projective algebraic varieties. Genus of plane smooth algebraic curves. 
Exercises from Lecture 14 psfile , pdffile 
Topological classification of surfaces by Richard Koch. 

A note on summability (in German) by Günther Trautmann. 
Forster, Otto.  Lectures on Riemann surfaces; transl. by Bruce Gilligan, New York: SpringerVerlag, 1999.  
Schlichenmaier, Martin.  An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces, Berlin: Springer, 2007.  
Freitag, Eberhard; Busam, Rolf.  Complex analysis. Transl. from the German by Dan Fulea, Berlin: Springer, 2009.  
Freitag, Eberhard.  Complex analysis 2. Riemann surfaces, several complex variables, Abelian functions, higher modular functions, Berlin: Springer, 2011.  
Miranda, Rick.  Algebraic curves and Riemann surfaces, Providence RI: American Mathematical Society, 1995.  
Farkas, Hershel M.; Kra, Irwin.  Riemann surfaces, Springer, 1992.  
Griffiths, Philip; Harris, Joseph.  Principles of algebraic geometry, New York : J. Wiley, 1994. 