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PENA, C. A. de C.. Estudo global de sistemas polinomiais planares no disco de Poincaré. 2015. 45 pp. Dissertação (Mestrado em Ciências – Matemática) – Instituto de Ciências Matemáticas e de Computação (ICMC/USP), São Carlos – SP. Given a planar differential system, many questions are raised about the behavior of their solutions. In the neighborhood of singular points there exist many tools which indicate their type and their structural stability; they are known as normal forms. However, the interest goes beyond the local behavior in the neighborhood of each singularity. In this dissertation we present some classical tools from the qualitative theory of ordinary differential equations which are usually applied to the global investigation of planar polinomial vector fields and we apply them to the investigation of two parametric families of quadratic fields from the study of the vector fields with invariant hyperbolas. Among the studied tools we highlight the local classification of the solutions around elementary and semi-elementary singular points and the technique known as Poincaré’s compactification. Key-words: planar polinomial differential systems; invariant algebraic curves; Poincaré’s compactification; local classification of singular points; global phase portraits