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This book is my master project at National University Malaysia (UKM). In this research, the main objective is to study the class Mp of meromorphically p-valent functions on the unit disk with positive and negative coefficients. We introduced some new classes by using certain linear operator. Then we investigated various important properties for these subclasses such as coefficients inequalities and inclusion properties, the radii of starlikeness, convexity, neighborhood properties, the subordination and superordination, and integral operator.