This lecture overviews Decision Surfaces and, in particular, Support Vector Machines that have many applications in Machine Learning and Pattern Recognition. It covers the following topics in detail: Decision surfaces. Hyperplanes. Non-linear Decision Surfaces. Quadratic (2nd degree polynomial) surfaces, Hyperellipsoid/Hyperparaboloid. Support Vector Machines, Margin Maximization, Lagrangian Primal/Dual Problem, Kernel SVM.