This paper concerns propagation of surface waves along a plasma column, and their amplification by interaction with an electron beam penetrating the plasma. First, surface wave propagation is analyzed for stationary and drifting plasmas. In addition to undamped propagation, the dispersion relation describes infinite sets of modes which can be categorized as evanescent and damped propagating waves. Next, it is shown how surface waves can be driven unstable by an electron beam. When the beam partially fills the plasma, interaction may occur not only with surface waves but also with plasma oscillations. A detailed stability analysis for the case of beam filling the plasma shows that the system may be either convectively or absolutely unstable, depending on the beam parameters. These findings are compared with the predictions of weak coupled mode theory, which are demonstrated to be misleading. Experiments aimed at measuring surface wave amplification, and checking the theory, are described. The propagation observed is interpreted as a beating between a weakly growing and a damped surface wave. The maximum growth corresponded to an electronic gain of 2 dB/cm at 470 MHz. The paper concludes with a brief discussion of the applicability of the results to development of a practical beam/plasma microwave amplifier.