One common problem in machine learning is to train a computer to correctly classify some data set when the potential set of features is known. However, the problem of classification becomes even more tricky if an adversary gains access to the input data set and can modify the features. In this talk, I will first present some adversarial examples to motivate the problem. Then, I will introduce the adversarial training problem for binary classification and discuss the geometric and analytic techniques we use to study its minimizers.