Maximum likelihood estimation is one of the most popular methods for estimating parameters in parametric models. It was introduced, studied, and popularized by Ronald Fisher, one of the greatest statisticians of all time. Maximum likelihood estimates are known to be very powerful and have many attractive properties, especially when the sample size is large. In this chapter, we will provide the intuition behind this method, define the likelihood function and the maximum likelihood estimate, consider several classical examples, and discuss the main properties of the method.