**[Cr:4, Lc:3, Tt:1, Lb:0]**

- Noetherian rings and Noetherian modules, Hilbert basis theorem, affine space and algebraic sets, ideal of a set of points, algebraic subsets of a plane, Hilbert's Nullstellensatz, integral and algebraic extensions.
- Coordinate rings, affine coordinate transformations, discrete valuation rings, ideals with finitely many zeros, multiple points, tangent lines and local rings.
- Projective space and projective algebraic sets, affine and projective varieties, product spaces, linear system of curves and Bézout's theorem, Max Noether's theorem.
- The Zariski topology, morphism of varieties, algebraic function fields and dimension of varieties, rational maps.
- Rational maps of curves, blowing up of a point in
and
, quadratic transformations and non singular model curves.
- Divisors, Riemann's theorem and the genus of a non singular model curve, derivations and differentials, canonical divisors and the Riemann-Roch theorem.

- William Fulton , Algebraic Curves, http://www.math.lsa.umich.edu/ wfulton/.
- Igor R. Shafarevich, Basic Algebraic Geometry I, Springer, Third Edition.

- C. Musili, Algebraic Geometry for Beginners, Hindustan Book Agency.