In this thesis we study several properties of Learning Vector Quantization. LVQ is a nonparametric detection scheme proposed in the neural network community by Kohonen. We examine it in detail, both theoretically and experimentally, to determine its properties as a nonparametric classifier. In particular, we study the convergence of the parameter adjustment rule in LVQ, we present a modification to LVQ which results in improving the convergence of the algorithms, we show that LVQ performs as well as other classifiers on two sets of simulations, and we show that the classification error associated with LVQ can be made arbitrarily small.