Viro’s patchworking technique

We look at real plane algebraic curves. As a topological space, such a curve is a disjoint union of ovals and, if the curve has odd degree, a pseudoline. We discuss Viro’s patchworking technique, which is a combinatorial process that generates plane real algebraic curves with prescribed topology. We then use this patchworking to generate maximal curves, which are curves having the maximum possible number of connected components.