From Trajectories to Ensembles in Classical Mechanics -- Dynamics of Open Classical Systems -- Elements of Quantum Mechanics -- Optics and Quantum Mechanics -- Dynamics of Open Quantum Systems -- Quantum Mechanics with Trajectories -- Trajectories in Optics -- Calculus of Variations -- Stochastic processes.

Trajectory-based formalisms are an intuitively appealing way of describing quantum processes because they allow the use of "classical" concepts. Beginning at an introductory level suitable for students, this two-volume monograph presents (1) the fundamentals and (2) the applications of the trajectory description of basic quantum processes. This first volume is focussed on the classical and quantum background necessary to understand the fundamentals of Bohmian mechanics, which can be considered the main topic of this work. Extensions of the formalism to the fields of open quantum systems and to optics are also proposed and discussed.