1 아핀다양체 Affine varieties and their basic properties 2 사영다양체 Projective varieties and homogeneous coordinates 3 준사영다양체 Quasi-projective varieties and regular maps 4 유리사상 Rational maps and birational equivalence 5 차원 Dimension of algebraic varieties 6 접공간과 매끄러움 Tangent spaces and smoothness of algebraic varieties 7 그라스만 다양체 Grassmannians as parameter spaces of linear subspaces 8 인자 Weil divisors, Cartier divisors, and divisor class groups 9 선다발과 벡터다발 Line bundles, invertible sheaves, and the Picard group 10 선형계 Complete linear systems, base loci, and ampleness 11 표준선다발 Canonical bundle and canonical divisor 12 층 코호몰로지 Sheaf cohomology and its applications 13 사영공간의 코호몰로지 Bott’s formula and the cohomology of line bundles on projective space 14 세르 쌍대성 Serre duality theorem and its applications 15 곡선에서의 리만-로흐 정리 The Riemann–Roch theorem for curves 16 곡면에서의 리만-로흐 정리 Intersection theory on surfaces and its applications 17 고다이라 소멸정리 Kodaira vanishing theorem과 그 응용 18 저우 군 Chow groups and the cycle class map 19 교차곱 The intersection product on Chow groups 20 베주 정리 Bézout’s theorem and its applications