This book gives an up-to-date account of progress on Pansu's celebrated problem
on the sub-Riemannian isoperimetric profile of the Heisenberg group. It also
serves as an introduction to the general field of sub-Riemannian geometric
analysis. It develops the methods and tools of sub-Riemannian differential
geometry, nonsmooth analysis, and geometric measure theory suitable for attacks
on Pansu's problem.