Title: High precision measurements of the neutron spin structure in HallA at JLab Abstract: The long standing quest for the origin of the spin of the nucleon is going to take a remarkable leap at the Thomas Jefferson National Laboratory in the coming years. JLab is undergoing an important upgrade which will double the maximum energy of its high intensity longitudinally polarized electron beam by the beginning of 2014. The beam will be delivered simultaneously on the 3 existing experimental halls (adequately upgraded) and a new hall dedicated to real photon physics. An intense physics program will exploit the advantages offered by the new JLab experimental equipment to investigate the nucleon spin structure, in terms of high accuracy and extended phase space. In this respect, high luminosity experiments will be carried on in the Hall A on a polarized 3He target (effective neutron target) in the Deep Inelastic Scattering limit. An inclusive measurement with unprecedented precision will be devoted to the determination of the photon asymmetry A1n at large $x_{Bjorken} \sim 0.71$ in the valence region, where perturbative QCD calculations exist and are sensitive to the quark Orbital Angular Momentum (OAM) contributions to the nucleon wave function. Moreover, combination of these new data with measurements on the proton will permit a flavor decomposition of the polarization of the parton distribution functions. This will be likely one of the early experiments at JLab after the energy upgrade. In addition, the first high statistics determination of the neutron single spin asymmetry in semi inclusive scattering of pion and kaon off transversely polarized 3He target is also expected to run in Hall A, using the newly developed high luminosity, large acceptance Super BigBite Spectrometer (SBS). The neutron single spin asymmetry, at leading twist, is related to the Transversity and Sivers quark distribution functions which are sensitive to the relativistic effects inside the nucleon and the quark OAM contribution respectively. Both experiments will benefit of new GEM (Gas Electron Multiplier) tracking detectors able to operate in the high background flux expected in high luminosity experiments. In the talk, theoretical and experimental details of the above two precise measurements will be presented.