This paper presents a fully quantum theory of cavity-assisted sideband cooling of mechanical motion, focusing on a cantilever coupled via radiation pressure to an optical cavity. The theory derives the opto-mechanical cooling rate and the minimum achievable phonon number by analyzing the quantum noise of the radiation pressure force. It shows that achieving arbitrarily small phonon numbers requires operating in the "good cavity" regime, where the cavity linewidth is much smaller than the mechanical frequency and cavity detuning. This contrasts with the common assumption that the mechanical frequency and cavity detuning should be comparable to the cavity damping. The paper discusses the two main cooling approaches: active feedback-based cooling and passive, non-feedback-based cooling. The latter involves parametric coupling between the cantilever and a driven resonator, allowing the cantilever to be cooled to lower energy states. The cooling rate depends on the resonator's quantum fluctuations, which compete with the cooling process. The paper presents a quantum mechanical description of the self-cooling of a cantilever coupled to an optical cavity via radiation pressure. This system is of interest due to its simplicity and experimental realization. The results are valid for both the good-cavity and bad-cavity regimes. The paper also shows that it is possible to cool the cantilever to its quantum mechanical ground state by choosing the cantilever resonance frequency much larger than the cavity ring-down rate, a regime not previously considered. The paper derives the power spectrum of the noise and shows that the asymmetry in the noise spectrum leads to cooling or heating. The radiation pressure noise is non-equilibrium but can be assigned a unique effective temperature under certain conditions. The paper also discusses the optomechanical frequency shift ("optical spring effect") and its relation to the force spectrum. The paper compares the results with simpler models and shows that the correct quantum-mechanical result requires a detuning-dependent effective decay rate. The paper also presents an exact solution of the linearized Heisenberg equations of motion for the mechanical and optical degrees of freedom, allowing for the discussion of the strong cooling regime. The results show that the cantilever can be cooled to arbitrarily small phonon numbers in the far-detuned regime, where the mechanical frequency is much larger than the cavity linewidth. This regime avoids the bistability that can interfere with cooling in some current schemes. The paper concludes that the full quantum theory of cavity-assisted sideband cooling of a cantilever has been developed, providing a basis for future optomechanical experiments in the quantum regime of mechanical motion.This paper presents a fully quantum theory of cavity-assisted sideband cooling of mechanical motion, focusing on a cantilever coupled via radiation pressure to an optical cavity. The theory derives the opto-mechanical cooling rate and the minimum achievable phonon number by analyzing the quantum noise of the radiation pressure force. It shows that achieving arbitrarily small phonon numbers requires operating in the "good cavity" regime, where the cavity linewidth is much smaller than the mechanical frequency and cavity detuning. This contrasts with the common assumption that the mechanical frequency and cavity detuning should be comparable to the cavity damping. The paper discusses the two main cooling approaches: active feedback-based cooling and passive, non-feedback-based cooling. The latter involves parametric coupling between the cantilever and a driven resonator, allowing the cantilever to be cooled to lower energy states. The cooling rate depends on the resonator's quantum fluctuations, which compete with the cooling process. The paper presents a quantum mechanical description of the self-cooling of a cantilever coupled to an optical cavity via radiation pressure. This system is of interest due to its simplicity and experimental realization. The results are valid for both the good-cavity and bad-cavity regimes. The paper also shows that it is possible to cool the cantilever to its quantum mechanical ground state by choosing the cantilever resonance frequency much larger than the cavity ring-down rate, a regime not previously considered. The paper derives the power spectrum of the noise and shows that the asymmetry in the noise spectrum leads to cooling or heating. The radiation pressure noise is non-equilibrium but can be assigned a unique effective temperature under certain conditions. The paper also discusses the optomechanical frequency shift ("optical spring effect") and its relation to the force spectrum. The paper compares the results with simpler models and shows that the correct quantum-mechanical result requires a detuning-dependent effective decay rate. The paper also presents an exact solution of the linearized Heisenberg equations of motion for the mechanical and optical degrees of freedom, allowing for the discussion of the strong cooling regime. The results show that the cantilever can be cooled to arbitrarily small phonon numbers in the far-detuned regime, where the mechanical frequency is much larger than the cavity linewidth. This regime avoids the bistability that can interfere with cooling in some current schemes. The paper concludes that the full quantum theory of cavity-assisted sideband cooling of a cantilever has been developed, providing a basis for future optomechanical experiments in the quantum regime of mechanical motion.