Tutorial theme: This tutorial will develop mathematical models for the spread of infectious diseases by starting with the most basic dynamic models and then increasing the complexity to include host-vector situations, multiple groups, variable population size, age-structure, differential-delay equations, and functional differential equations. The models presented will address concepts such as thresholds, basic reproduction numbers, stability of equilibria, global stability, Hopf bifurcation to periodic solutions, multiple endemic equilibria, and chaotic behavior. Applications to specific diseases such as tuberculosis, influenza, rubella, chickenpox, whooping cough, and HIV/AIDS will be included. Thus, the essentials of model formulation and mathematical analysis will be presented, examples of the use of models to answer questions about specific diseases will be examined, and some of the questions, challenges, and opportunities in theoretical epidemiology will be discussed. This tutorial course will be accessible to mathematicians who want to learn about epidemiology modeling and to epidemiologists who want to learn about dynamic modeling of infectious disease transmission and control.