We are at a very special point in space and time. The Large Hadron Collider has experienced a first very successful physics run that culminated with the discovery of the long sought-after Higgs boson. We have begun probing the substructure of nature at unprecedented 10^(-17) cm distances, corresponding to the energy scales of the few TeV. The goal of this project is to develop a formalism to bring the study of the recently discovered Higgs boson into a precision era. With the discovery last year of a new resonance that is identified as the long sought-after Higgs boson with a probability better than 1-10^(-13), a new era started in the understanding of the Standard Model (SM) of particle physics. In the absence of any evidence for any other new degree of freedom at the weak scale, a mass gap is likely to separate the SM particles from the dynamics generating and stabilizing the Higgs potential. Our ignorance about the New Physics sector can thus be conveniently parametrized in terms of a set of higher dimensional operators built out of the SM blocks and obeying the simple SM symmetries laws. The Higgs data collected by the ATLAS and CMS experiments (as well as by the 2 Tevatron experiments) start putting interesting bounds on the 8 unconstrained deformation directions affecting the Higgs physics. Two lines of research will be developed in this project: 1/ the identification of the best variables to characterize the Higgs data in analogy with the oblique parameters that were introduced to study EW data, 2/ the computation of next-to-leading corrections for the Higgs production and decay rates in the presence of higher dimensional operators deforming the SM.