This document provides an introduction to differentials and infinitessimals. It discusses how differentials represent infinitesimal changes in calculus and how they can be understood through the hyperreal number system containing nonzero infinitesimals. While differentials are essentially zero with respect to real numbers, their ratios and sums can provide finite results. The document cautions that differentials cannot always be canceled and provides an example using discontinuous functions to illustrate this point. It concludes by summarizing the appropriate conditions for canceling differentials.