Optomechanics was born on the theory side in the late 70s, in the framework of high-sensitivity measurements, and especially gravitational-wave detection, when Braginsky, Caves and others discussed the impact of quantum fluctuations of light on the sensitivity of the envisioned large-scale gravitational-wave interferometers. But experimental optomechanics only appeared some 20 years later, to become a mature and very active research field only very recently, when progress in laser sources (stability and low-noise operation), micro- and nanofabrication, low-loss coatings and low-vibration cryogenics allowed optomechanical operation closer to the quantum regime. The focus can be either on the quantum properties of light (optomechanical squeezing), on the mechanical resonator (experimental observation of the mechanical quantum ground state), or on both, with the ambitious goal of entanglement between a mechanical resonator and the light field, or between two mechanical resonators through radiation pressure. Our project aims for a number of milestones in the field, on every facet of optomechanics. Gathering experience and expertise among 4 different laboratories (LKB: active and pioneering group in the field, LPN: cutting-edge facilities and expertise in nanofabrication, LMA: worldwide leader in low-loss optical coatings, ONERA: international expertise in ultra-stable mechanical resonators), the collaboration established here, with expertise spanning the whole experimental process, is essential to the effective fulfilment of any particular experiment, but it has the potential as well to achieve them all. The project will help the collaboration to strengthen its current position in the international competition and to establish firm experimental foundations for future works deep into the quantum regime of optomechanics. We will take advantage of the modifications of the light inside a moving mirror cavity to demonstrate optomechanical squeezing, with unique features such as a frequency-dependent squeezed quadrature. Also, laser cooling in a high-finesse cavity will be used to demonstrate the quantum-mechanical ground state of a dedicated optomechanical resonator, taking advantage of the fact that, unlike condensed-matter systems, optomechanical resonators offer clear signatures of the ground state. Both envisioned experiments are obviously strongly related, even though they require specific optimization of the optomechanical resonator. Optomechanical properties of a different system, an optomechanical crystal with unique on-chip integration features, will be investigated as well and used to cool it to its fundamental state. On a longer term, it is worth noting that the observation of such quantum phenomena with macroscopic objects is not only of great interest from a conceptual point of view, but also is the key prerequisite for the preparation of non-classical states of motion, and, on a more technological level, for the development of micro and nanomechanical sensors with an unprecedented sensitivity, only limited by quantum noises. Applications are expected in the fields of single-molecule detection, optical switches, or in quantum hybrid systems for storage and transfer of quantum information.