With the availability of high frequency financial data, new areas of research in stochastic modeling and stochastic control have opened up. This course will introduce some of the concepts, questions and methods that arise in this domain. We will begin with a description of the basic elements of electronic markets, some of the features of the data, its empirical implications and simple microeconomic models. Next, we will investigate algorithmic trading problems from the stochastic optimal control perspective, including the optimal execution problem and show how to modify the classical approaches to include order-flow information and the effect that dark pools have on trading. Electronic markets would not exist without market markets, so we next investigate how market markers with various trading goals and constraints post orders optimally. Trading pairs of assets that mean-revert is another important algorithmic strategy, and we will see how stochastic control methods can be utilized to inform agents how to optimally trade.