Classical sampling theorem establishes the relationship between the band-limited signal and its uniform samples. This paper reinforces it in three aspects. First, the error formula of the reconstructed signal and the original signal is presented when the theorem conditions are not satisfied. Second, this paper analyzes the uniform sampling of the band-pass signal using concise method, and then gets the conditions which the sampling frequency should satisfy. Last, the nonuniform sampling of the band-pass signal is studied. The consent range for sampling frequency and the reconstructed formula from its nonuniform samples are presented. All this enriches and deepens the classical sampling theorem.