This is a reading seminar of a graduate student, following the Fields medal work of Daniel Quillen on the foundation of the higher algebraic K-theory.

6 students (four advanced undergraduate students and two first year graduate students) present their summer study results on the subject of algebraic curves and Riemann surfaces. The topic include: - On sheaves and cohomology over topological spaces. - On relationship between divisors and line bundles on compact Riemann surfaces. - On holomorphic vector bundles on compact Riemann surfaces. - On Cech cohomology of sheaves on compact Riemann surfaces. - On Serre duality theorem on compact Riemann surfaces. - On the Riemann-Roch theorem on compact Riemann surfaces.