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.