This tutorial introduces Gaussian process regression (GPR) as a powerful, non-parametric Bayesian approach for modeling, exploring, and exploiting unknown functions. GPR is particularly useful in scenarios where the underlying function is complex, difficult to evaluate analytically, or where design costs are high. The tutorial covers the mathematical foundations of GPR, including the concept of distributions over functions and the role of kernels in encoding prior assumptions. It demonstrates GPR's application in various contexts, such as modeling mouse trajectories, compositional response time analysis, and exploration-exploitation problems. The tutorial also discusses the optimization of hyperparameters and the use of acquisition functions for active learning. Finally, it provides examples and references for further exploration.This tutorial introduces Gaussian process regression (GPR) as a powerful, non-parametric Bayesian approach for modeling, exploring, and exploiting unknown functions. GPR is particularly useful in scenarios where the underlying function is complex, difficult to evaluate analytically, or where design costs are high. The tutorial covers the mathematical foundations of GPR, including the concept of distributions over functions and the role of kernels in encoding prior assumptions. It demonstrates GPR's application in various contexts, such as modeling mouse trajectories, compositional response time analysis, and exploration-exploitation problems. The tutorial also discusses the optimization of hyperparameters and the use of acquisition functions for active learning. Finally, it provides examples and references for further exploration.