Abstract : In the field of the inertial confinement fusion ( ICF), the equation of state ( EoS) of the hydrogen and its isotopes is one of the most important properties to know. The EoS based on chemical models have difficulty in giving an unambiguous description of the hydrogen in the strong coupled and partial degenerate regime, called Warm Dense Matter ( WDM). Indeed, these models use potential with adjustable parameters to describe the many body interactions which are important in the WDM. On the other hand, the ab initio methods resolve almost exactly the quantum many body problem and are thus particularly relevant in this domain. In the first part of this thesis, we describe how we built a table of a multi-phase EoS of the hydrogen, using ab initio methods in the field of the WDM. We show in particular that this EoS is in very good agreement with most of the available experimental data (principal Hugoniot, sound velocity in the molecular fluid, melting curve at low pressure, measurements of multiple shocks). In the second part, we present a direct application of our EoS by showing its influence on the criteria of ignition and combustion of two target designs for ICF: a self-ignited target which will be used on the Laser MegaJoule ( LMJ), and a shock-ignited target. We show in particular that the optimization of the laser pulse allowing maximizing the thermonuclear energy is strongly dependent on the precision of the EoS in the strong coupled and degenerate domain.