Electron spectroscopy (ES) of the surface of a solid comprises a set of methods of studying its elemental composition, structure, electronic structure, and dynamics. The essence of almost all the methods consists in obtaining and studying the energy spectra and angular distributions of electrons emitted by the surface of the solid upon irradiation with fluxes of photons, electrons, or ions, or upon creating a strong electric field near it. Depending on the nature of the probe, one can distinguish photoelectron, secondary-electron, ion-electron, and field spectroscopy. Each of them is realized by several methods. In practically all the methods analysis of the characteristics that are obtained consists of singling out certain unitypical elementary events of interaction of the probe agent with the surface layers of the solid. As a rule, the depth of probing is determined by the mean free path of the electron with respect to inelastic interaction. In the electron energy range from tens to approximately hundreds of electron volts in various materials, it constitutes from one to several atomic layers. In determining elemental composition, the sensitivity of most of the ES methods is approximately equal to hundredths of a monolayer. One can employ a scanning probe to obtain the distribution of the elements over the surface of the specimen. Most of the ES methods have been invented in the past decade. At present the studies in the field of surface physics are intensively developing and have great scientific and important applied significance. This review briefly treats the physical fundamentals of the ES methods, their potentialities, classifies the methods, gives examples to illustrate them, and cursorily throws light on the fundamental technical means of realizing the methods.