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The paper is devoted to the questions connected with the investigation of theS.P. Novikov problem of the description of the geometry of level lines ofquasiperiodic functions on a plane with different numbers of quasiperiods. Weconsider here the history of the question, the current state of research inthis field, and a number of applications of this problem to various physicalproblems. The main attention is paid to the applications of the resultsobtained in the field under consideration to the theory of transport phenomenain electron systems.

Topological integrability, classical and quantum chaos, and the theory of dynamical systems in the physics of condensed matter