Bohmian Mechanics was found 1952 by David Bohm as an ontological theory of quantum phenomena. It had been revived in the second half of the last century by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. The theory is about the motion of point particles, the statistical analysis of which, yields the formalism of quantum mechanics in terms of Hilbert spaces, self-adjoint operator-observables, and projection and positive operator valued measures. Tunneling times, arrival times, and first exit times are easily described within Bohmian mechanics.The book explains how Boltzmann 's probabilistic reasoning in statistical mechanics when applied to Bohmian mechanics leads to a rational account of quantum mechanics and its mathematical abstractions. It provides the insight and the mathematical tools to establish the formalism of quantum theory, including scattering theory, as the statistical macroscopic description of Bohmian mechanics.
It reviews the essentials of classical physical theories relevant to the probabilistic reasoning and introduces Bohmian mechanics from various points of views. It provides rational perspectives on identical particles (bosons and fermions), the classical limit, quantum equilibrium, uncertainty relation and quantum observables. The book is self contained, it develops carefully the insight for the need of the mathematics of quantum mechanics, which is carried out with full mathematical rigor.