Abel’s theorem, abelian varieties, Jacobians, theta functions, Clifford’s theorem, Castelnuovo’s quota, Noether’s theorem, extreme curves, Enriques-Babbage theorem, Petri’s theorem, the varieties of special divisors W_r^d and G^r_d, Brill-Noether theory.

References
E. Arbarello, M. Cornalba, P. A. Griffiths, J. Harris, Geometry of Algebraic Curves, Vol. 1, Springer Verlag, 1985.
D. Eisenbud, J. Harris, The Practice of Algebraic Curves, Graduate Studies in Mathematics, Vol. 250, AMS, 2024.