The logical fundamentals of the theory of climate are outlined: (1) the climate system OLA (ocean-land-atmosphere) is defined; (2) analogously to the theory of turbulence, the notion of climate is defined as a multicomponent random function in the OLA space-time (or, equivalently, as a statistical ensemble of states the OLA system passes through in a period of several decades); (3) the solar climate, i.e. the distribution of solar radiation at the upper atmosphere boundary, is determined, to be employed as the boundary condition for the OLA system; (4) the ’horizontal’ heat and mass transfer processes between the equatorial and polar zones are described; (5) the ’vertical’ processes of radiative-convective heat and mass transfer, among them the greenhouse effect of water vapor and small gas admixtures, are discussed; (6) the ’vertical’ radiative heat transfer processes in an aerosol-containing atmosphere is considered, including the anti-greenhouse effect of volcanic and smoke aerosols, and the ’nuclear night’ and ’nuclear winter’ scenarios.