SPIRou is a near-infrared (nIR) spectropolarimeter / velocimeter proposed as a new-generation instrument for CFHT. SPIRou aims in particular at becoming world-leader on two forefront science topics, (i) the quest for habitable Earth-like planets around very- low-mass stars, and (ii) the study of low-mass star and planet formation in the presence of magnetic fields. In addition to these two main goals, SPIRou will be able to tackle many key programs, from weather patterns on brown dwarf to solar-system planet atmospheres, to dynamo processes in fully-convective bodies and planet habitability. The science programs that SPIRou proposes to tackle are forefront (identified as first priorities by most research agencies worldwide), ambitious (competitive and complementary with science programs carried out on much larger facilities, such as ALMA and JWST) and timely (ideally phased with complementary space missions like TESS and CHEOPS). SPIRou is designed to carry out its science mission with maximum efficiency and optimum precision. More specifically, SPIRou will be able to cover a very wide single-shot nIR spectral domain (0.98-2.35 mu m) at a resolving power of 73.5K, providing unpolarized and polarized spectra of low-mass stars with a ~15% average throughput and a radial velocity (RV) precision of 1 m/s.