Classification algorithms have been widely used in many application domains. Most of these domains deal with massive collection of data and hence demand classification algorithms that scale well with the size of the data sets involved. A classification algorithm is said to be scalable if there is no significant increase in time and space requirements for the algorithm (without compromising the generalization performance) when dealing with an increase in the training set size. Support Vector Machine (SVM) is one of the most celebrated kernel based classification methods used in Machine Learning. An SVM capable of handling large scale classification problems will definitely be an ideal candidate in many real world applications. The training process involved in SVM classifier is usually formulated as a Quadratic Programing (QP) problem. The existing solution strategies for this problem have an associated time and space complexity that is (at least) quadratic in the number of training points. It makes SVM training very expensive. This thesis addresses the scalability of the training algorithms involved in SVM to make it feasible with large training data sets.