This material introduces the basic theory of maximum likelihood estimation by discussing the likelihood function, the log likelihood function, and maximizing these functions using calculus. Several exercises ask students to derive certain estimators, while others have students compare the behavior of those estimators with other possibilities through the use of various JAVA applets. The applets use the same control features: the sliders set the parameter values, the “Stop #” drop down menu sets the number of samples taken, the “Update #” drop down menu sets how often the graph and tables update during the experiment, the single arrow takes one sample, the double arrow runs the full experiment, the square stops the experiment, and the back arrow resets the applet. This page is one lesson from the Virtual Laboratories in Statistics.