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Introduction Chapter one. Fundamental Definitions and Basic Concepts Introduction 1.1 Fundamental Definitions 1.2 Basic Concepts Chapter Two. Some Properties of Certain Subclasses of Univalent and Meromorphic Univalent and Multivalent Functions Defined by Subordination Property with Some Operators Introduction 2.1 Some Geometric Properties of a Certain Subclass of Univalent Functions Defined by Differential Subordination Property 2.2 Some Interesting Properties of a New Class of Univalent Functions Defined by Ruscheweyh Derivative 2.3 On a New Class of Meromorphic Univalent Functions defined by linear operator 2.4 Certain Results of a New Class of Meromorphic Multivalent Functions Involving Ruscheweyh Derivative Chapter Three. On New classes of Univalent and Uniformly Convex Functions with Negative Coefficients by Using Fractional Calculus Techniques Introduction 3.1 Fractional Calculus Operators Associated with a Certain Class of Uniformly Convex Functions 3.2 On a New Class of Univalent Functions with Applications of Fractional Calculus Operators Defined by Hohlov Operator Chapter Four. Some Results of Certain Classes of Harmonic Univalent Functions Introduction 4.1 A certain Class of Harmonic Univalent Functions Defined by Integral Operator 4.2 Some Results on Analytic Part of Harmonic Univalent Functions Chapter Five. On Differential Subordination Properties of Univalent and Multivalent Functions Defined by Ruscheweyh Derivative Operator Introduction 5.1 Strong Differential Subordination Properties for Multivalent Functions Defined by Ruscheweyh Derivative Operator 5.2 On Second �COrder Differential Subordinations for Univalent Functions Associated with Ruscheweyh Derivative Operator References �༭�ּ�