Abstract
The initial objective of this research project is to study the concepts and basic results of the Qualitative Theory of Ordinary Differential Equations. We will approach local and global aspects of the theory such as: Existence and Uniqueness Theorem, Tubular Flow Theorem, Stable Manifold Theorem, Grobman-Hartman's Theorem, Poincaré's First Return Map, and Poincaré-Bendixson's Theorem. In …