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Dynamical properties and synchronization of chaotic and hyperchaotic systems involving real variables have been studied and investigated in applied sciences over the last 30 years. There is, however, a wide variety of the physical problems which, from mathematical point of view, can be studied more conveniently by using complex variables. The dynamics of these systems is rich and complex. The aim of this monograph is to introduce and analyze some chaotic and hyperchaotic complex nonlinear systems. The basic dynamical properties of these systems are presented. The control problem of hyperchaotic attractors of these systems is also stated. Several types of synchronization of chaotic and hyperchaotic complex nonlinear dynamical systems are investigated in this monograph. This monograph is mainly addressed to graduate students and senior researchers interested in the study of chaotic and hyperchaotic complex (or real) nonlinear dynamical systems.