and Acknowledgements.- I. Thermodynamic Relations in Crystalline Solutions.- 1. Crystalline Solutions.- 2. Choice of a Chemical Component.- 3. General Properties of Solutions.- a) Chemical Potential.- b) Ideal Crystalline Solution.- c) Non-Ideal Solutions and Excess Functions of Mixing.- d) Chemical Potential and Activity of a Component in a Mineral.- II. Thermodynamic Models for Crystalline Solutions.- 1. Regular Solution Model.- a) Zeroth Approximation.- b) Simple Mixture Model.- c) Quasi-Chemical Model.- 2. General Relations for Binary, Ternary, and Quaternary Nonideal Crystalline Solutions.- III. Thermodynamic Stability of a Solution.- 1. Critical Mixing.- 2. General Conditions.- a) Simple Mixture.- b) General Nonideal Solution.- 3. Spinodal Decomposition.- 4. Critical Mixing in Quasi-Chemical Approximation.- 5. Immiscibility in Ternary Crystalline Solutions.- 6. Formation of Miscibility Gaps in a Ternary Simple Mixture.- 7. Formation of Miscibility Gap in Asymmetric Ternary Solutions.- 8. Immiscibility in Mineral Systems.- a) Interpretation of Sequences of Mineral Assemblages.- b) Intrinsic and Extrinsic Stability.- c) Immiscibility in Garnets.- IV. Composition of Coexisting Phases.- 1. Ideal Solution Model.- a) Distribution of a Component between Two Ideal Binary Crystalline Solutions.- b) Coexisting Ternary Ideal Solutions.- 2. Nonideal Solutions.- a) Distribution of a Component between Two Simple Mixtures.- b) Coexisting Regular Ternary Solutions.- 3. Distribution of a Cation between Two or More Multicomponent Minerals.- 4. Composition of Coexisting Minerals and Chemical Equilibrium in Igneous Rocks.- 5. Physico-Chemical Conditions of Formation of Mineral Assemblages as Inferred from Composition of Coexisting Phases.- 6. Stability of Orthopyroxene.- 7. Distribution of Trace Elements.- V. Measurement of Component Activity Using Composition of Coexisting Minerals.- 1. Compositional Data Available on a Complete Distribution Isotherm.- 2. Composition Data on a Cl“Z