||The subjects of this thesis are the invisible axion and the more general family of axion-like particles. The invisible axion is a hypothetical elementary particle and a cold dark matter candidate. I present an improved computation of the constraints on the parameter space of the cold dark matter axion in the standard cosmology, that includes the contributions from anharmonicities in the axion potential and from the decay of axionic strings. In this scenario, I update the value of the mass of the cold dark matter axion, fi nding the value (67 ± 17)µeV, approximately one order of magnitude larger than previous computations. The eff ect of nonstandard cosmological scenarios on the parameter space of axion cold dark matter is studied for the first time. In particular, I consider the cases of low-temperature reheating and kination cosmologies, and I show that the mass of the cold dark matter axion can differ from the value in the standard cosmological scenario by orders of magnitude. Finally, I consider the family of axion-like particles, assuming that these particles serve as the inflation in the context; of warm inflation. I find that the axion energy scale f, which in the standard inflation scenario is of the order of the Planck mass, can be lowered to the much safer Grand Uni cation Theory scale f ~ 1016GeV. I also constrain the parameter space and the amount of gravitational waves from this model, using results from the Wilkinson Microwave Anisotropy Probe 7-year data.