Compulsory Topics:

- Affine and projective spaces, in particular, the projective line and the projective plane,
- Plane algebraic curves over the complex numbers,
- Smooth and singular points,
- Bézout's Theorem for projective plane curves,
- Topological genus of a curve and the genus formula,
- Rational maps between plane curves and the Riemann-Hurwitz formula.

In addition, a selection of the following topics is covered:

- Polar and Hessian curves,
- Dual curves and Plücker’s formulas,
- Linear systems and divisors on smooth curves,
- Real projective curves,
- Puiseux-parameterizations of plane curve singularities,
- Invariants of plane curve singularities,
- Elliptic curves,
- Further aspects of plane algebraic curves.

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