  We explore Arnold's $J^+$-invariant of immersions -- planar smooth closed
curves with non-vanishing derivative, at most double points and only transverse
intersections -- and computation methods like Viro's sum, among others. Only
basic undergraduate mathematics is needed to understand the contents of this
introductory paper and everything we need that is above that is recalled or
introduced. Examples, exercises and solutions are included for practice.
