Mass Conservation -- Conservation of Momentum -- Derivatives for the Equations of State -- On the Variety of Notations of the Energy Conservation for Single-phase Flow -- First and Second Laws of the Thermodynamics -- Some Simple Applications of Mass and Energy Conservation -- Exergy of  Multi-Phase Multi-Component Systems -- One-Dimensional Three-Fluid Flows -- Detonation Waves Caused by Chemical Reactions or by Melt-Coolant Interactions -- Conservation Equations In General Curvilinear Coordinate Systems -- Type of the System of PDEs -- Numerical Solution Methods for Multi-Phase Flow Problems -- Numerical Methods for Multi-Phase Flow in Curvilinear Coordinate Systems -- Conservation Equations in the Relative Coordinate System -- Visual Demonstration of the Method.