Support Vector Machines have met with significant success in numerous real-world learning tasks. However, like most machine learning algorithms, they are generally applied using a randomly selected training set classified in advance. In many settings, we also have the option of using pool-based active learning. Instead of using a randomly selected training set, the learner has access to a pool of unlabeled instances and can request the labels for some number of them. We introduce an new algorithm for performing active learning with Support Vector Machines, i.e., an algorithm for choosing which instances to request next. We provide a theoretical motivation for the algorithm. We present experimental results showing that employing our active learning method can significantly reduce the need for labeled training instances in both the standard inductive and transductive settings.