LHCb is one of the four main experiments hosted at the Large Hadron Collider (LHC) at CERN. The LHC first started in September 2008 and, after a one-year hiccough, restarted in November 2009. In the course of three weeks, the HEP community witnessed the first LHC proton-proton collisions and a new record of the most energetic particle beam. The ease shown by the operators of the complex LHC machine augurs very well for the extended period of data-taking scheduled to start at the end of February 2010. LHCb is the LHC experiment primarily dedicated to the b realm, through the study of CP violation and rare decays. Its physics goals are ambitious: it aims at the indirect search of New Physics and at the precise measurements of CP violation parameters. The LHCb detector was designed as a single-arm forward spectrometer. The branching fraction of the yet-unobserved Bs0 → μ+ μ- decay is currently considered as one of the most stringent tests for the existence of physics beyond the Standard Model (SM) of particle physics. There exists indeed a large unexplored range between the current experimental upper limit and the SM prediction about this branching fraction, making a measurement incompatible with the SM possible. Furthermore, there exist predictions for this branching fraction in the frame of numerous theoretical models that aim at a more accurate description of matter than that offered by the Standard Model. Some of those predictions significantly differ from the SM one, opening the possibility of an indirect discovery of New Physics. In this thesis, I present the study of the sensitivity of the LHCb experiment to this branching fraction with Monte Carlo simulations. I show that LHCb will compete with the Tevatron for the exclusion limit of the Bs0 → μ+ μ- branching fraction already in 2010 and that approximately 3fb-1 at √s = 14TeV are enough for a 3σ evidence of a SM signal. In a particle physics experiment, the precise measurement of the charged particle trajectories is essential. Indeed tracking gives experimental access to their momentum and allows the reconstruction of the physical properties of the short-lived particle of which they are the decay products. The Inner Tracker is the detector that provides tracking information for the particles ying in the innermost part of LHCb. Because of its central position, the Inner Tracker calls for the use of very light-weighted material which compete with the precision and rigidity required by such a detector. During my thesis work, I contributed to the construction of the Inner Tracker through the set up of an assembly procedure for the detector boxes, uncovering several design aws and contributed to solve them pragmatically. I defined quality requirements at key steps of the assembly and implemented tests to assess them. I conducted the assembly of the twelve Inner Tracker detectors boxes that were installed in the LHCb cavern in Summer 2008. After software alignment, the overall precision of the Inner Tracker modules position is on average 19 µm along the relevant direction. The careful box assembly and the quality tests along the procedure allowed to keep the dead strips fraction below 1 %. Finally, tracks from the LHC collisions have been seen!