This book reviews the basics of Support Vector Machines (SVM), their evolution and applications in diverse fields. SVM is an efficient supervised learning approach popularly used for pattern recognition, medical image classification, face recognition and various other applications. In the last 25 years, a lot of research has been carried out to extend the use of SVM to a variety of domains. This book is an attempt to present the description of a conventional SVM, along with discussion of its different versions and recent application areas. The first chapter of this book introduces SVM and presents the optimization problems for a conventional SVM. Another chapter discusses the journey of SVM over a period of more than two decades. SVM is proposed as a separating hyperplane classifier that partitions the data belonging to two classes. Later on, various versions of SVM are proposed that obtain two hyperplanes instead of one. A few of these variants of SVM are discussed in this book. The major part of this book discusses some interesting applications of SVM in areas like quantitative diagnosis of rotor vibration process faults through power spectrum entropy-based SVM, hardware architectures of SVM applied in pattern recognition systems, speaker recognition using SVM, classification of iron ore in mines and simultaneous prediction of the density and viscosity for the ternary system water ethanolethylene glycol ionic liquids. The latter part of the book is dedicated to various approaches for the extension of SVM and similar classifiers to a multi-category framework, so that they can be used for the classification of data with more than two classes.