This paper provides an introduction to Gaussian Process (GP) regression models, focusing on the role of the stochastic process and its application in defining distributions over functions. The authors explain how to incorporate training data and learn hyperparameters using the marginal likelihood. They highlight the practical advantages of GPs, such as their flexibility and ease of use, compared to traditional parametric models. The paper covers the definition of GPs, their posterior distribution, and the process of training a GP model by optimizing hyperparameters through the marginal likelihood. It also discusses the automatic Occam's razor property, which simplifies training by penalizing complex models. The authors conclude by discussing future directions, including the use of different covariance functions and handling non-Gaussian likelihoods, and acknowledge the computational challenges and ongoing research in these areas.This paper provides an introduction to Gaussian Process (GP) regression models, focusing on the role of the stochastic process and its application in defining distributions over functions. The authors explain how to incorporate training data and learn hyperparameters using the marginal likelihood. They highlight the practical advantages of GPs, such as their flexibility and ease of use, compared to traditional parametric models. The paper covers the definition of GPs, their posterior distribution, and the process of training a GP model by optimizing hyperparameters through the marginal likelihood. It also discusses the automatic Occam's razor property, which simplifies training by penalizing complex models. The authors conclude by discussing future directions, including the use of different covariance functions and handling non-Gaussian likelihoods, and acknowledge the computational challenges and ongoing research in these areas.