In this elementary talk we'll introduce the Kahler differentials and see some of their applications in algebraic geometry. First we will use them to define what it means for a variety to be smooth at a point. Then, we will make use of them to define the algebraic de Rham cohomology of an affine algebraic variety. We will compute some examples and see more interesting applications as time permits. The talk should be accessible to students currently in the algebraic geometry sequence. Speaker(s): Andrew Odesky (UM)