This book deals with systems of polynomial autonomous ordinary
differential equations in two real variables. The emphasis is mainly
qualitative, although attention is also given to more algebraic aspects
as a thorough study of the center/focus problem and recent results on
integrability. In the last two chapters the performant software tool P4
is introduced. From the start, differential systems are represented by
vector fields enabling, in full strength, a dynamical systems approach.
All essential notions, including invariant manifolds, normal forms,
desingularization of singularities, index theory and limit cycles, are
introduced and the main results are proved for smooth systems with the
necessary specifications for analytic and polynomial systems.