Support Vector Machines (SVMs) solve binary classification by finding the maximum-margin separating hyperplane. In the hard margin setting for linearly separable data, the dual formulation reveals that solutions depend only on support vectors, which are training points on the margin. For non-separable data, soft margins introduce slack variables and penalty parameter C, balancing margin width against misclassification tolerance. The kernel trick enables nonlinear decision boundaries through implicit feature mapping. Brief coverage of alternative classifiers includes Naive Bayes, k-Nearest Neighbors, Random Forests, and Neural Networks.