This chapter discusses Hamiltonian Monte Carlo (HMC), a Markov Chain Monte Carlo (MCMC) method that uses Hamiltonian dynamics to generate proposals for the Metropolis algorithm. HMC avoids the slow exploration of the state space that occurs with simple random-walk proposals by using Hamiltonian dynamics, which preserves volume and allows for complex mappings without needing to account for a Jacobian factor. The method involves introducing fictitious "momentum" variables and using them to define a Hamiltonian function that combines potential and kinetic energy. The HMC algorithm alternates between updating momentum variables and using Hamiltonian dynamics to propose new states, which can be distant from the current state but have a high probability of acceptance. The method is described in detail, including the use of the leapfrog scheme for discretizing Hamiltonian equations, and variations such as using windows of states for acceptance, approximate trajectory computation, tempering, and shortcut methods. The chapter also discusses the theoretical and practical aspects of HMC, including its volume preservation, reversibility, and symplecticness, and how these properties ensure that the method leaves the desired distribution invariant. The chapter concludes with examples illustrating the efficiency of HMC compared to simple random-walk Metropolis methods.This chapter discusses Hamiltonian Monte Carlo (HMC), a Markov Chain Monte Carlo (MCMC) method that uses Hamiltonian dynamics to generate proposals for the Metropolis algorithm. HMC avoids the slow exploration of the state space that occurs with simple random-walk proposals by using Hamiltonian dynamics, which preserves volume and allows for complex mappings without needing to account for a Jacobian factor. The method involves introducing fictitious "momentum" variables and using them to define a Hamiltonian function that combines potential and kinetic energy. The HMC algorithm alternates between updating momentum variables and using Hamiltonian dynamics to propose new states, which can be distant from the current state but have a high probability of acceptance. The method is described in detail, including the use of the leapfrog scheme for discretizing Hamiltonian equations, and variations such as using windows of states for acceptance, approximate trajectory computation, tempering, and shortcut methods. The chapter also discusses the theoretical and practical aspects of HMC, including its volume preservation, reversibility, and symplecticness, and how these properties ensure that the method leaves the desired distribution invariant. The chapter concludes with examples illustrating the efficiency of HMC compared to simple random-walk Metropolis methods.