Support Vector Machines (SVM) are known as the state of the art learning algorithms. Although they are called as the state of the art learning algorithms, the kernel functions take an important place when the SVM performance is the main concern. Recently Chebyshev kernel has been proposed as a good alternative to the well known and used Gaussian kernel. Therefore in this book we studied this kernel functions as well as several other kernel functions, and compared their performances. We also proposed a generalization method to use Chebyshev kernels on vector inputs directly. Moreover, we also discussed some properties of Gaussian kernels when used with SVM.