About half a century ago Landau formulated the central principles of the phe­ nomenological second-order phase transition theory which is based on the idea of spontaneous symmetry breaking at phase transition. By means of this ap­ proach it has been possible to treat phase transitions of different nature in altogether distinct systems from a unified viewpoint, to embrace the aforemen­ tioned transitions by a unified body of mathematics and to show that, in a certain sense, physical systems in the vicinity of second-order phase transitions exhibit universal behavior. For several decades the Landau method has been extensively used to an­ alyze specific phase transitions in systems and has been providing a basis for interpreting experimental data on the behavior of physical characteristics near the phase transition, including the behavior of these characteristics in systems subject to various external effects such as pressure, electric and magnetic fields, deformation, etc. The symmetry aspects of Landau's theory are perhaps most effective in analyzing phase transitions in crystals because the relevant body of mathemat­ ics for this symmetry, namely, the crystal space group representation, has been worked out in great detail. Since particular phase transitions in crystals often call for a subtle symmetry analysis, the Landau method has been continually refined and developed over the past ten or fifteen years.

1. Introduction to Phenomenological Phase Transition Theory.- 1. Fundamentals of Landau's Thermodynamic Theory.- 2. Prerequisites on Space-group Representations.- References.- 2. Physical Realization of the Order Parameters at a Microscopic Level of Description.- 3. Tensor Representation of the Space Group on a Basis of Localized Atomic Functions.- 4. Permutational Representation and its Basis.- 5. Vector Representation and its Basis.- 6. Pseudovector Representation and its Basis.- References.- 3. Symmetry Change at Phase Transitions.- 7. Change in Translational Symmetry.- 8. The Total Symmetry Change.- 9. Domains.- 10. The Paraphase.- References.- 4. Analysis of the Thermodynamic Potential.- Invariant Expressions of the Thermodynamic Potential.- 12. Integral Rational Basis of Invariants.- 13. Examples of the Construction of an IRBI.- 14. Irreducible Representation Images and Thermodynamic Potential Types.- 14. Irreducible Representation Images and Thermodynamic Potential Types.- 5. Phase Diagrams in the Space of Thermodynamic Potential Parameters.- 15. Theoretical Fundamentals of the Phase Diagram Construction Method.- 16. The One-Component Order Parameter.- 17. The Two-Component Order Parameter.- 19. The Role of the IRBI in the Construction of Phase Diagrams.- 20. Coupling Order Parameters.- References.- 6. Macroscopic Order Parameters.- 21. Transformation Properties of the Order Parameters.- 22. Interplay of Micro- and Macroparameters.- 23. Ferroics.- 24. Non-ferroics.- References.- 7. Phase Transitions in an External Field.- 25. Phase Diagrams.- Features Peculiar to the Temperature Behavior of Susceptibility in the Vicinity of the Second-Order Phase Transition.- Calculation of Susceptibilities for Second-Order Phase Transitions.- Singularities of theSusceptibility in the Vicinity of the First-Order Phase Transition.- 29. Domains in an External Field.- References.- 8. Martensite Transformations.- 30. Reconstructive Structural Transitions.- 31. Thermodynamic Analysis of the Homogeneous State.- 32. Inhomogeneous States in the Vicinity of the Phase Transition.- 33. The Omega Phase.- References.- 9. Incommensurate Periodicity Phases.- 34. General Approach to the Problem.- 35. Phases without Linear Gradient Terms in Free Energy.- 36. Phases with Linear Gradient Terms.- 37. Multi-?-structures.- 38. Incommensurate Phases in External Fields.- 39. The Thermodynamics of Phase Transitions to Incommensurate Phases.- References.- 10. Color Symmetry and its Role in Phase Transition Theory.- 40. Color Symmetry in the Theory of Magnetic Structures.- 41. Supersymmetry of Incommensurate Structures.- 42. Icosahedral Symmetry of Crystals. Quasicrystals.- 43. Color Groups in the Theory of Systems with a Quantum Mechanical Order Parameter.- References.- 11. Fluctuations and Symmetry.- 44. Fundamentals of the Fluctuation Phase Transitions Theory.- 45. Critical Behavior of Anisotropic Systems.- 46. Fluctuation-Induced Break-Down to First-Order Phase Transitions.- 47. Fluctuations in the Vicinity of Multicritical Points.- References.