Review of the modern status of investigations of the problem of phase transitions in cold nuclei between nuclear states of a different geometrical shape is presented. In the framework of the Interacting Boson Model phase transitions between different nuclear shapes are considered in the space of the three control parameters which are parameters of the Hamiltonian of the model. Depending on the values of these parameters equilibrium shape of a nucleus can be spherical, axially deformed or triaxial. It is shown that on the phase diagram of a nucleus, which is Casten triangle, in fact, spherical phase is separated from the axially deformed phases by the lines of the first order phase transitions. Also two deformed phases with different signs of axial deformation are separated one from the other, by the line of the first order phase transition. These lines come together in the triple point where the second order phase transition takes place. A question of dynamical symmetries in the critical points is considered. Experimental information on nuclei whose properties are close to those predicted for the critical points of the phase transitions is discussed. It is shown that the phase transition from axially symmetric to triaxial deformation is a second order phase transition. In the framework of the Bohr-Mottelson model an approximate solution describing nucleus near the critical point of the spherical-triaxially deformed phase transition is found.

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