Geometry and Probability in Banach Spaces Type and cotype for a Banach space p summing maps Pietsch factorization theorem Completely summing maps. Hilbert Schmidt and nuclear maps p integral maps Completely summing maps: Six equivalent properties. p Radonifying maps Radonification Theorem p Gauss laws Proof of the Pietsch conjecture p Pietsch spaces. Application: Brownian motion More on cylindrical measures and stochastic processes Kahane inequality. The case of Lp. Z type Kahane contraction principle. p Gauss type the Gauss type interval is open q factorization Maureys theorem Grothendieck factorization theorem Equivalent properties summing vs. factorization Non existence of (2+) Pietsch spaces Ultrapowers The Pietsch interval. The weakest non trivial superproperty. Cotypes Rademacher vs. Gauss Gauss summing maps. Completion of grothendieck factorization theorem. TLC and ILL Super reflexive spaces. Modulus of convexity q convexity trees and Kelly Chatteryji Theorem Enflo theorem. Modulus of smoothness p smoothness. Properties equivalent to super reflexivity Martingale type and cotype. Results of Pisier. Twelve properties equivalent to super reflexivity. Type for subspaces of Lp (Rosenthal Theorem).