Luca Capogna & Donatella Danielli 
An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem [PDF ebook] 

The Isoperimetric Problem in Euclidean Space.- The Heisenberg Group and Sub-Riemannian Geometry.- Applications of Heisenberg Geometry.- Horizontal Geometry of Submanifolds.- Sobolev and BV Spaces.- Geometric Measure Theory and Geometric Function Theory.- The Isoperimetric Inequality in ?.- The Isoperimetric Profile of ?.- Best Constants for Other Geometric Inequalities on the Heisenberg Group.