We introduce an operator formalism for random sequential adsorption on lattices and in continuous space. This provides a convenient framework for deriving series expansions for the deposition rate dθ/dt in powers of t. Several specific examples - the square lattice with nearest-neighbor exclusion, and with exclusion extended to next-nearest neighbors, and disks and oriented squares on the plane-are considered in detail. Precise estimates for θ(t) and the jamming coverage are obtained via Padé approximant analysis. These are found to be in excellent agreement with simulation results. A diagrammatic expansion for dθ/dt is derived, and its relation to the equilibrium Mayer series is elucidated.