Metal surface plasmon is a collective oscillation effect of free electrons at the micro-nanostructure surface under the stimulation of incident light. Since the corresponding oscillating electric field is strongly bound below the sub-wavelength scale, it can be used as an information carrier for future micro-nano photonic circuit and device, and can also be used to enhance the interaction between light and matter on a micro-nano scale, such as surface enhanced photoluminescence, Raman scattering, nonlinear signal generation, surface enhanced catalysis, photothermal conversion, photovoltaic conversion, etc. How to theoretically understand the unique optical behavior dominated by the plasmon oscillation mode is one of the hot research spots in the field of surface plasmon photonics. In recent years, the theory of surface plasmon has been continuously improved with the support of a large number of experimental researches. In this paper, we first systematically summarize the optical behaviors and properties of metal under the excitation of incident electromagnetic waves, and then briefly describe the plasmonic modes existing in the metal and their corresponding physical natures, the oscillation dynamics process and the currently prevailing surface plasmon coupling theories. We hope that this paper can provide a theoretical basis for those researchers who have just dabbled in the field of surface plasmons and help them to master the relevant basic knowledge quickly.