In the bulk of this book, we have avoided the rigorous formulation of stochastic processes used by probabilists. We have sacrificed the level of rigor in order to make the material accessible to applied mathematicians and biological physicists who tend not have a background in advanced probability theory. However, it is useful to have some exposure to the concepts and notation used by probabilists. Therefore, in this appendix, we give a very brief introduction to probability theory with an emphasis on martingales.