This PhD thesis is at a cross-road between three different fields : the spintronics which uses the spin degree of freedom of the electron to build new devices ; the molecular electronics which tries to take advantage of the new development of the chemistry, to give a workaround to the all semiconductor paradigm of the microelectronics industry; and the molecular magnetism which synthesizes molecular magnet with properties of an increasing richness. Our work has been dedicated to the fabrication of a molecular magnet based electronic device with which we could use the spin of the electron to study the magnetic properties at a single molecule level. Such device could, in the future, be used in the field of quantum information. We have decided to fabricate a field effect molecular transistor in which a well known molecular magnet, the Terbium double-decker or TbPc2, acts as a channel. Thanks to this device, we evidenced the quantum tunnelling of the magnetization (QTM) at single molecule level. We demonstrated that the magnetic moment reversal induces an abrupt change in the differential conductance of the system. By performing a statistical study, we highlighted four resonances that were attributed to QTM. We also measured a single nuclear spin state : each resonance being directly associated with one particular nuclear spin state. We studied the nuclear spin temperature and showed that it could be influenced by the electrostatic environment. Furthermore, the spin state lifetime was assessed and estimated to few seconds, highlighting the low invasive character of our measurement technique. This work give the foundation of the first molecular magnet based Qbit. With radio frequency techniques, the nuclear spin could be manipulated, the readout being performed through conductance measurement.