Plane algebraic curves
Gerd Fischer 
American Mathematical Society
Introduction. -- Affine algebraic curves and their equations. -- The projective closure. -- Tangents and singularities. -- Polars and Hessian curves. -- The dual curve and the Plücker formulas. -- The ring of convergent power series. -- Parametrizing the branches of a curve by Puiseux series. -- Tangents and intersection multiplicities of germs of curves. -- The Riemann surface of an algebraic curve. -- Appendix 1. The resultant. -- Appendix 2. Covering maps. -- Appendix 3. The implicit function theorem. -- Appendix 4. The Newton polygon. -- Appendix 5. A numerical invariant of singularities of curves. -- Appendix 6. Harnack's inequality