The basic thermodynamic theories of terrestrial dry and moist air are summarized. Atmospheric water vapor-liquid, vapor-ice and liquid-ice phase transitions using Clapeyron and Clausius-Clapeyron equations are presented in a coherent and clear way. Basic theory and several practical expressions to compute dew points and/or relative humidity are presented. Density altitude corrected for humidity can be easily computed from presented moist air thermodynamic relationships. Understanding thermodynamics and dynamics of atmospheric moist air and phase transitions is of fundamental importance for safety and economy of flight operations. Moist air plays significant role not only in atmospheric and cloud physics, but also for aircraft performance computations, human life support and environmental control systems.