  We present an introduction to the manifold calculus of functors, due to
Goodwillie and Weiss. Our perspective focuses on the role the derivatives of a
functor F play in this theory, and the analogies with ordinary calculus. We
survey the construction of polynomial functors, the classification of
homogeneous functors, and results regarding convergence of the Taylor tower. We
sprinkle examples throughout, and pay special attention to spaces of smooth
embeddings.
