This paper will discuss how a Gaussian process, which describes a probability distribution over an infinite dimensional vector space, can be implemented with finite computational resources. It will discuss how the hyperparameters controlling a Gaussian process can be adapted to data. We will then study a variety of different ways in which Gaussian processes can be constructed. Finally there will be an overview of advanced methods using Gaussian processes. It is surprising how much you can do with a single Gaussian distribution! 2. Nonlinear Regression