Contents: Introduction(3).The method of Ermakov(4).The method of Milne(7).
Pinney's result(8).Lewis' results(8). The interpretation of Eliezer and
Gray(14). The connection of the Ermakov invariant with N\"other's theorem(17).
Possible generalizations of Ermakov's method(20). Geometrical angles and phases
in Ermakov's problem(22). Application to the minisuperspace cosmology(26).
Application to physical optics(42).Conclusions(47). Appendix A: Calculation of
the integral of I(48). Appendix B: Calculation of <\hat{H}> in eigenstates of
\hat{I}(49).References(50).