Content: Introduction: The Buildings' Envelope-a Component of the Building Energy SystemSystematic Approach Applied to BuildingsEnvelope System (Envelope) and Energy Functions DesignSummary Analysis of the Building-Surrounding Energy InteractionsPhysics of Energy Conversions in the Building Envelope at Microscopic LevelIdealized Physical Model of the Building Envelope as an Energy-Exchanging Medium (Review of the Literature from Microscopic Point of View)Conclusions and Generalizations Based on the Survey of Literature Published in the FieldDesign of a Hypothetical Physical Model of Phonons Generation in Solids: Scatter of Solar Radiation within the SolidMicro-Macroscopic Assessment of the State of the Building EnvelopeDesign of a Model of Energy Exchange Running between the Building Envelope and the Surroundings: Free Energy PotentialEnergy-Exchange Models of the Building EnvelopeWork Done in the Building Envelope and Energy-Exchange ModelsSpecification of the Structure of the Free Energy in the Components of the Building Envelope (Electrothermodynamic Potential of the System)Distribution of the Free Energy within the Building EnvelopeDefinition of the Macroscopic Characteristics of TransferGeneral Law of TransferPhysical Picture of the Transmission PhenomenaConclusionsNumerical Study of Transport in Building Envelope ComponentsMethod of the Differential RelationsMethod of the Integral FormsWeighted Residuals Methodology Employed to Assess the ETS Free Energy FunctionInitial and Boundary Conditions of a Solid Wall ElementEffects of the Environmental Air on the Building EnvelopeVarious Initial and Boundary Conditions of Solid Structural ElementsDesign of Boundary Conditions of Solid Structural ElementsEngineering Methods of Estimating the Effect of the Surroundings on the Building Envelope: Control of the Heat Transfer through the Building Envelope (Arrangement of the Thermal Resistances within a Structure Consisting of Solid Wall Elements)Calculation of the Thermal Resistance of Solid Structural Elements by means of Indexes of Energy efficiencySolar Shading Devices (Shield) CalculationModeling of Heat Exchange between a Solar Shading Device, a Window, and the SurroundingsDesign of Minimal-Size of Windows by means of the Coefficient of DaylightMethod of Reducing the Tribute of the Construction and the Thermal Bridges to the Energy InefficiencyAssessment of Leaks in the Building Envelope and the Air-Conditioning Systems by Delta_Q methodMathematical Model of the Environmental Sustainability of Buildings and its employment in BG_LEED method AcknowledgmentsApplication (Solved Tasks in 1D, 2D and 3D FE and Tables)Matrix of Conductivity [K(1)]Matrix of Surface Properties [F(1)]Generalized Matrix of the Element Conductivity [G(1)] = [K(1)] + [F(1)]Vector of a Load due to Recuperation Sources {fc(1)} Vector of a Load due to Convection to the Surrounding Matter {fc(1)}Vector of a Load due to a Direct Flux {fDre}