Introduction to Plane Algebraic Curves Book

1	Affine algebraic curves	3
2	Projective algebraic curves	13
3	Coordinate ring of an algebraic curve	23
4	Rational functions on algebraic curves	31
5	Intersection multiplicity and intersection cycle of two curves	39
6	Regular and singular points of algebraic curves : tangents	51
7	More on intersection theory : applications	61
8	Rational maps : parametric representations of curves	73
9	Polars and Hessians of algebraic curves	81
10	Elliptic curves	89
11	Residue calculus	99
12	Applications of residue theory to curves	117
13	The Riemann-Roch theorem	131
14	The genus of an algebraic curve and of its function field	143
15	The canonical divisor class	149
16	The branches of a curve singularity	161
17	Conductor and value semigroup of a curve singularity	175
	Algebraic foundations	189
A	Graded algebras and modules	191
B	Filtered algebras	199
C	Rings of quotients : localization	209
D	The Chinese remainder theorem	217
E	Noetherian local rings and discrete valuation rings	221
F	Integral ring extensions	227
G	Tensor products of algebras	235
H	Traces	245
I	Ideal quotients	257
K	Complete rings : completion	261
L	Tools for a proof of the Riemann-Roch theorem	275