1 The Early Topological Study of Real Algebraic Plane Curves

• 1.1 Basic Definitions and Problems
• 1.2 Digression: the Topology of Closed One-Dimensional Submanifolds of the Projective Plane
• 1.3 Bézout's Prohibitions and the Harnack Inequality
• 1.4 Curves of Degree $\le 5$
• 1.5 The Classical Method of Constructing Nonsingular Plane Curves
• 1.6 Harnack Curves
• 1.7 Digression: the Space of Real Projective Plane Curves
• 1.8 End of the Proof of Theorem 1.6.A
• 1.9 Isotopy Types of Harnack $M$-Curves
• 1.10 Hilbert Curves
• 1.11 Analysis of the Results of the Constructions. Ragsdale
• 1.12 Generalizations of Harnack's and Hilbert's Methods. Brusotti. Wiman
• 1.13 The First Prohibitions not Obtained from Bézout's Theorem
• Exercises