Cosmic inflation is a family of theories for the physics of the very early universe that remedy a number of deficiencies of the naive hot Big Bang model (the monopole, horizon, flatness, and smoothness problems). Inflation also provides a mechanism for generating the primordial cosmological perturbations through quantum fluctuations. The dynamics of a scalar field in an expanding universe is explored and it is explained how inflation resolves the defects of the naive hot Big Bang model. The Bunch–Davies vacuum for a scalar field in de Sitter space is derived. The theory of linear cosmological perturbations about ahomogeneous slow roll solution is derived and the predicted primordial power spectra for both the scalar and the tensor perturbations are derived. Higher-order corrections in the slow roll approximation as well as calculations beyond the slow roll approximation are described.