Mathematics knowledge grows every day; new discoveries and overwhelming amounts of new information make it more and more difficult to write comprehensive yet informative texts. This one developed as an attempt to pin down the basics of stochastic differential equations （SDE's）， simple questions like， \"What is a stochastic differential equation?\" It turns out the depth behind the requisite knowledge to answer such an elementary question is quite substantial.
　　Many great texts already exist that attack SDE's from the stochastic perspective， but our main objective is to present the material from the dynamical systems perspective， aimed at the audience familiar with classical analysis and differential equations. Really， my advisor Paul Schmidt at Auburn University had the idea of presenting the material from a \"new cultural perspective\" and his contribution to this work is enormous. We feel that this presentation will help mathematicians understand， with a minimum of technicality， what SDE's are， and if they are appropriate for their particular modeling/applications.