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The object of this book is to study certain classes of analytic functions in the open unit disk in the complex plane . This book consists of five chapters: The first chapter is the introduction of the book which contains some definitions , notations and principle lemmas which are used in this book. The second chapter, is to define and study certain classes of analytic functions with complex order, some properties of these classes are also obtained . The third chapter introduces and studies a family of bounded analytic functions with complex order, this chapter contains certain properties of the functions which belong to this family. The fourth chapter contains some applications of some analytic functions defined by a number of differential operators. The last chapter contains several subclasses of analytic functions defined by a linear operator. Moreover the results of this book generalize and improve many results studied before.