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This book deals with some function spaces and classes of analytic and hyperbolic-type. We study two kinds of complex-valued function spaces as follows: First, we study general classes of functions the so called Q_{k,w}(p; q)- type classes. For these classes, we obtain: Characterizations in terms of Carleson measures. Characterizations by the help of Hadamard gap class. Some important inequalities related to these classes with some other classes of analytic functions. Moreover for these classes: We study Hadamard products defined by integral norms acting between functions belonging to these classes. Secondly, we apply some certain operators on function spaces and classes of hyperbolic-type. Further, we introduce some new weighted hyperbolic classes of functions. These classes are shown to be complete quasi-metric spaces with respect to the corresponding metrics. Moreover, necessary and sufficient conditions are given for the composition and superposition operator to be bounded andcompact