This volume contains lecture notes on key topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics.

PDEs in Conformal Geometry.- Heat Kernels in Sub-Riemannian Settings.- Concentration of Solutions for Some Singularly Perturbed Neumann Problems.- On Some Elliptic Problems in the Study of Selfdual Chern-Simons Vortices.- The k-Hessian Equation.- Minimal Surfaces in CR Geometry.