This book introduces analysis and numerical study for three different types of bifurcation. The first type which belongs to local bifurcation is Hopf bifurcation and the other two types are homoclinic and heteroclinic belong to global bifurcations. Moreover, bifurcation analysis and chaos control in two different nonlinear dynamical systems with Delayed Feedback control will be discussed. In this work, we use powerful tools and important theoretical criterions such as: (The undetermined coefficient method, the complementary-cluster energy-barrier criterion, the first Lyapunov coefficient, the si'lnikov criterion, center manifold theory, Cardan formula, Descarte's rule of signs and time- delayed feedback control) in order to introduce a local analysis for Hopf bifurcation in the Liu system, and a global analysis for existence of si'lnikov orbits, Smale horseshoes and the horseshoe type of chaos in the Lü system , the Zhou's system and in the 3-D chaotic system only with two stable node-foci. Moreover, the Zhou's system and Schimizu-Morioka system will be controlled using time-delayed feedback control.