Geometric Analysis and PDEs 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. This volume contains lecture notes on some 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. The presentation of the material should be rather accessible to non experts in the field since the presentation is didactic in nature. The reader will be provided with a survey containing some of the most exciting topics in the field with a series of techniques used to treat such problems.