Polynomial rings over fields, Hilbert basis theorem, Maximal ideals in polynomial rings over
algebraically closed fields and Hilbert’s Nullstellensatz, affine algebraic sets, affine algebraic varieties,
projective varieties.

Morphisms of varieties and rational maps, Local rings and germs of functions on varieties, krull
dimension of rings and dimension of varieties, Nonsingular varieties, Jacobian criterion.
Sheaves, locally ringed spaces, schemes, morphisms of schemes.