Bayesian methods play a key role in modern statistical modelling. The main aim of Bayesian nonparametric methods is to avoid dependence on critical parametric assumptions, thus robustifying parametric models, and also to provide a sensitivity analysis for such models by embedding them in a broader nonparametric model. This course introduces Bayesian nonparametric methods, and particular emphasis will be placed on models based on Dirichlet processes and Polya trees, with a view towards applications and software implementation. Special attention will be given to density estimation and regression, along with application in biostatistics.