Using the mathematical theory of Brownian motion, this book develops in detail the statistical basis of nonequilibrium thermodynamics. In particular, it is shown that thermodynamic criteria emerge in the limit of small thermal fluctuations and in the Gaussian limit where means and modes of the distribution coincide. The theory of Brownian motion is assumed to be a rather general and useful model of irreversible processes that are inevitably influenced by random thermal fluctuations. The unifying approach adopted allows widely applicable principles to be extracted from the analysis of particular models. The content is arranged by argument rather than by chronology. It is based on the premise that random thermal fluctuations play a decisive role in governing the evolution of nonequilibrium thermodynamic processes. They can also be viewed as a dynamic superposition of a large number of random events with the important proviso that the future evolution depends only on the present, independent of its entire past history.