This tutorial introduces Gaussian process regression (GPR) as a powerful, non-parametric Bayesian method for modeling, exploring, and exploiting unknown functions. GPR is particularly useful in scenarios where the underlying function is unknown, and where the goal is to either explore the function to learn it or exploit it to make predictions. The tutorial covers the mathematical foundations of GPR, including how different kernels encode prior assumptions about the function, and how GPR can be applied in various settings such as optimal experimental design, Bayesian optimization, and safe exploration. GPR models functions as distributions over functions, allowing for probabilistic predictions and uncertainty quantification. The key components of GPR include the mean function, covariance function (kernel), and the use of Bayesian inference to update the model as new data is observed. The tutorial explains how GPR can be used to model functions in different ways, including through the weight space view and the function space view. It also discusses how to encode prior assumptions about the function's smoothness and periodicity using different kernels, such as the radial basis function (RBF) kernel and the Matérn kernel. The tutorial provides examples of GPR applications, including modeling mouse trajectories, analyzing response time patterns, and using GPR for active learning and exploration-exploitation scenarios. It also addresses the challenge of safe exploration, where additional constraints must be considered, such as avoiding outputs below a certain threshold. The tutorial concludes with a summary of recent psychological experiments using GPR to assess human function learning and highlights the importance of choosing appropriate kernels and hyper-parameters for different applications. Overall, the tutorial aims to provide a comprehensive yet accessible introduction to GPR for both theoretical and practical applications.This tutorial introduces Gaussian process regression (GPR) as a powerful, non-parametric Bayesian method for modeling, exploring, and exploiting unknown functions. GPR is particularly useful in scenarios where the underlying function is unknown, and where the goal is to either explore the function to learn it or exploit it to make predictions. The tutorial covers the mathematical foundations of GPR, including how different kernels encode prior assumptions about the function, and how GPR can be applied in various settings such as optimal experimental design, Bayesian optimization, and safe exploration. GPR models functions as distributions over functions, allowing for probabilistic predictions and uncertainty quantification. The key components of GPR include the mean function, covariance function (kernel), and the use of Bayesian inference to update the model as new data is observed. The tutorial explains how GPR can be used to model functions in different ways, including through the weight space view and the function space view. It also discusses how to encode prior assumptions about the function's smoothness and periodicity using different kernels, such as the radial basis function (RBF) kernel and the Matérn kernel. The tutorial provides examples of GPR applications, including modeling mouse trajectories, analyzing response time patterns, and using GPR for active learning and exploration-exploitation scenarios. It also addresses the challenge of safe exploration, where additional constraints must be considered, such as avoiding outputs below a certain threshold. The tutorial concludes with a summary of recent psychological experiments using GPR to assess human function learning and highlights the importance of choosing appropriate kernels and hyper-parameters for different applications. Overall, the tutorial aims to provide a comprehensive yet accessible introduction to GPR for both theoretical and practical applications.