In this thesis a single atom is trapped in the mode of a high-finesse cavity and used to generate single photons in a controlled way. Starting from a magneto-optical trap, rubidium atoms are loaded into an optical dipole-force trap and transported to the cavity. On arrival the atoms are trapped in another trap with a standing wave geometry and excited by a pump laser incident perpendicular to the cavity axis. With the help of cavity cooling forces, a single atom could then be selected and trapped for up to a minute. A sequence of laser pulses is applied to induce the emission of a stream of single photons from the atom. Up to 300000 photons could be generated from the same atom in this way. The single-photon character of the source is verified within a few seconds after which the photons can be distributed to an independent user while monitoring the presence of the atom.