The chapter introduces Monte Carlo methods, particularly focusing on their application in Bayesian inference. It begins by explaining the need for numerical integration in Bayesian inference, where the posterior distribution is often complex and analytically intractable. The chapter reviews basic Monte Carlo algorithms such as rejection sampling, importance sampling, and Markov Chain Monte Carlo (MCMC) methods. It provides theoretical justifications and practical advice for each method, emphasizing the importance of choosing appropriate proposal distributions to ensure efficient sampling. The chapter then delves into advanced MCMC techniques, including adaptive MCMC, which tunes the proposal distribution during the simulation, and transdimensional MCMC, which handles models with different numbers of parameters. It also discusses label switching issues in MCMC and how to address them using relabeling algorithms. Finally, the chapter concludes with a summary of the algorithms covered and a reference to Murray’s integration ladder, which outlines the progression from basic to advanced Monte Carlo methods in terms of complexity and applicability. The chapter aims to provide a comprehensive guide for practitioners in experimental physics and related fields, offering both theoretical insights and practical implementation tips.The chapter introduces Monte Carlo methods, particularly focusing on their application in Bayesian inference. It begins by explaining the need for numerical integration in Bayesian inference, where the posterior distribution is often complex and analytically intractable. The chapter reviews basic Monte Carlo algorithms such as rejection sampling, importance sampling, and Markov Chain Monte Carlo (MCMC) methods. It provides theoretical justifications and practical advice for each method, emphasizing the importance of choosing appropriate proposal distributions to ensure efficient sampling. The chapter then delves into advanced MCMC techniques, including adaptive MCMC, which tunes the proposal distribution during the simulation, and transdimensional MCMC, which handles models with different numbers of parameters. It also discusses label switching issues in MCMC and how to address them using relabeling algorithms. Finally, the chapter concludes with a summary of the algorithms covered and a reference to Murray’s integration ladder, which outlines the progression from basic to advanced Monte Carlo methods in terms of complexity and applicability. The chapter aims to provide a comprehensive guide for practitioners in experimental physics and related fields, offering both theoretical insights and practical implementation tips.