Support Vector Machines (SVMs) are binary classifiers that have been used in a wide variety of applications. One of the qualities that make SVMs popular is their ability to utilize a diverse class of similarity measures (kernel functions), which makes them sufficiently flexible to handle many different classification problems. This talk will offer an introduction to both linear and nonlinear SVMs, and discuss techniques that allow for the use of kernels that do not satisfy Mercer's condition, primarily the method proposed by Luss and d'Aspermont in their paper of the same name. No knowledge of SVMs is assumed.