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This lecture covers the basics of Support Vector Machines (SVM), starting with an introduction to SVM and its role in classification algorithms. The instructor explains the concept of Hinge Loss and its application in correctly classifying data points. The lecture delves into optimizing hyperplane separation and dealing with non-separable data using slack variables. It also explores the formulation of hard-margin SVM and the introduction of a penalty term for misclassifications. The lecture concludes with a discussion on non-linear classification using kernels and the dual form of the SVM problem.