For gravity wave trains propagating over an arbitrary wavy bottom, a perturbation expansion is developed to the third-order by employing three small perturbation parameters. Both the resonant and non-resonant cases are treated and the singular behavior at resonance is treated separately. All the theoretical results are presented in explicit forms and easy to apply. The bottom effects of different mean water depths and different degrees of undulation, as well as the steepness of incident waves, are clearly described by the theoretical results. In general non-resonant cases, the surface fluctuations deduced from undulated bottom topography decrease as the relative water depth increases and vice versa. The theory can be applied to the cases for wave trains propagating over wavy bottom topography with any arbitrary incident angles which are closer to natural phenomenon in coastal zone. Not only the well-known Bragg resonance but also the higher-order Bragg resonances are included in resonant cases. Unlike previous studies that analyze specific bottom topographies based on prescribed resonant conditions, both Bragg and higher-order Bragg resonances are revealed through the perturbation procedure step by step. For the resonant wave field, the amplification with propagating distance and time is revealed with the aid of the growth of energy flux. This theory is successfully verified by reducing to simpler situations. Also, the analytical results for the special case of two-dimensional wavy bottom are compared with experimental data for validation.