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The European Space Agency (ESA) and the National Aeronautics and SpaceAdministration (NASA) are planning the Laser Interferometer Space Antenna(LISA) mission in order to detect GW.  The need of accurate testing of free-fall and knowledge of noise in a spaceenvironment similar to LISA's is considered mandatory a pre-phase for theproject. Therefore the LISA Pathfinder mission has been designed by ESA to flythe LISA Technology Package (LTP), aiming at testing free-fall by measuring theresidual acceleration between two test-bodies in the dynamical scheme weaddress as "drag-free". The spectral map of the residual acceleration asfunction of frequency will convey information on the local noise level, thusproducing a picture of the environmental working conditions for LISA itself.  The thesis contains abundant material on the problem of compensating staticgravity, the development of a theory of orthogonalization of reference andcross-talk for the LTP experiment. The construction of the laser detectionprocedure starting from GR and differential geometry arguments is carried on.Effort was put in pointing out the physical motivations for the choices made inseveral other papers by the author and colleagues. In this perspective thethesis is meant as a summary tool for the LTP collaboration.  In the second part of the thesis we summarize our contributions for ameasurement of G onboard LTP and review on possible tests of fundamentalphysics the mission might embody.  A wide part of the thesis is now part of the LTP Operation Master Plan,describing the real science and operations onboard LISA Pathfinder. This thesiswas defended on September 26th, 2006 at the University of Como, Italy.

The LTP Experiment on LISA Pathfinder: Operational Definition of TT Gauge in Space