Abstract: A reasonable first approximation of a space X is its homology. Similarly, a first approximation to a functor F may be given by a homology theory, which is a particularly nice linear functor. This is the first stage of a Taylor tower of functors approximating F, developed by Goodwillie. One nice property of this tower is that within the ``radius of convergence'' of F, its value on a space X may be determined by the value of the limit of its Taylor tower on X. Functors of special interest are the identity functor of spaces and Waldhausen's Algebraic K-theory of a space, A(X). We will give an introduction to the calculus of functors, incorporating known results about these two functors.