Since the 1990s there has been significant activity in the theoretical development and applications of Support Vector Machines (SVMs). The theory of SVMs is based on the cross-pollenization of optimization theory, statistical learning, kernel theory, and algorithmics. So far, machine learning has largely been devoted to solving problems relating to data mining, text categorization, and pattern/facial recognition, but less so in the field of electromagnetics. Recently, popular binary machine learning algorithms, including support vector machines (SVM), have successfully been applied to wireless communication problems, notably spread spectrum receiver design and channel equalization. The aim of this book is to gently introduce SVMs in their linear and non linear forms, both as regressors and as classifiers, and to show how they can be applied to several antenna array processing problems and electromagnetics in general. The lecture is divided into three main parts. The first three chapters cover the theory of SVMs, both as classifiers and regressors. The next three chapters deal with applications in antenna array processing and other areas in electromagnetics. There are four appendices at the end of the book. The inclusion of MATLAB files will help readers start their application of the algorithms covered in the book.