The study of analytic functions has remained to be on the increase in the interest of researchers in the area of complex analysis. This is not unconnected with its wide applications in analysis and physical problems such as fluid flows, heat conditions, electrostatics, and potential as well as its interdependence role with many areas of mathematical endeavour. In the study of univalent functions,we are mainly interested in functions that are analytic.Many Authors have investigated the properties of subclasses of S and their results have several applications in engineering, hydrodynamic and signal theory. Some of their results have to do with the starlikeness and convexity properties of subclasses of univalent functions S.The aim of this present book is to study subclasses of univalent functions and to extend the results obtained by earlier researchers to more general functions.The results are been carefully arranged for easy understanding and research skills development for upcoming researchers in the area of analytic univalent functions and a good guide for researchers in other areas of mathematics. This monograph/book is therefore a must read for all upcoming researchers.