Abstract: This article introduced the training algorithm for the newest branch of statistic learning theory, SVM(Support Vector Machine),which can be classified into three categories: the first is the Decomposition Algorithm, whose delegate is SVMlight², the second is sequence algorithm, the third is online training algorithm. All the three kinds of algorithms' advantages and disadvantages were analysed. And other algorithms and multi-class algorithms are introduced too. The future direction and application of SVM in pattern recognition and data mining, and so on were introduced.