This tutorial is an introduction to mathematical modeling. Mathematical models for a variety of domains and applications will be developed, analyzed, and critically evaluated. Special emphasis will be given to models of the spread of infectious diseases. A variety of mathematical tools will be used, at the level of precalculus, calculus, and some elementary probability and graph theory. Some models will be explored with the help of custom-built software. Students will submit their work in the online meetings with the instructor. They will also submit a final modeling project.