A description of the theory and the mathematical base of support vector machines with a survey on its applications is first presented in this chapter. Then, a method for obtaining nonlinear kernel of support vector machines is proposed. The proposed method uses the gray wolf optimizer for solving the corresponding nonlinear optimization problem. A sensitivity analysis is also performed on the parameter of the model to tune the resulting classifier. The method has been applied to a set of experimental data for diabetes mellitus diagnosis. Results show that the method leads to a classifier which distinguished healthy and patient cases with 87.5% of accuracy.