Originating from research in the qualitative theory of ordinary
differential equations, this book follows the authors' work on
structurally stable planar quadratic polynomial differential systems. In
the present work the authors aim at finding all possible phase portraits
in the Poincaré disc, modulo limit cycles, of planar quadratic
polynomial differential systems manifesting the simplest level of
structural instability. They prove that there are at most 211 and at
least 204 of them.