The theory of electronic topological transitions

In the present review an attemp to survey all the theory of electronic topological transitions from the very first paper until the recent achievements is made. The presentation is started from the description of possible topological siguularities in electronic spectra of metals. Then the singularities of thermodynamical and transport properties of a metal in the vicinity of ETT, their fluctuations are discussed in details. In purpose to attract the wide reader audience, the transport phenomena including the behaviour of conductivity, thermoelectric power and sound absorption coefficient in the vicinity ETT are discussed in the framework of simple Boltzmann equation approach. The last chapter of the review are devoted to the discussion of the modern problems of ETT theory, application of it to the study of properties of 2D systems, quantum oscillations in magnetic field, generalized topological transitoins. The review is supplied by the extensive and complete bibliography including around 300 references.