The isotopy classification of affine quartic curves

In this paper we obtain the isotopyclassification of affine quartic curves, which contains 647 classes, and the topological classification of pairs (R², quartic curve), which contains 516 classes (see Theorem 7). We also present the isotopyclassifi cation of real projective quartic curves, which contains 66 classes. We prove that each of these classifications is equivalent to the classification of all real (affine or projective) quartic curves having onlys ingular points, if any, of types A₁, A*₁, D₄ or X₉ (see Theorems 5 and 6 and Corollaries 6.1-6.4).