This chapter explores Maximum Likelihood (ML) estimation, a statistical method used to estimate parameters of a given probability distribution. We begin with an introduction to the fundamental components of ML estimation, including the likelihood function, the density function, and the process of identifying parameter values that maximise the likelihood of the observed data. This chapter also covers numerical optimisation methods, both gradient-based and non-gradient, for situations where analytical solutions are impractical. We address sample variation in statistical estimation, highlighting the issues that may arise when relying on a single sample to infer population parameters, and review the use of simulation techniques, such as generating artificial datasets, to evaluate the reliability of these estimates.