The book is divided into two parts. The first part of less than 50 pages is devoted to a brief but clear and complete overview of phase-space quantization, described as an autonomous alternative formulation of quantum mechanics, besides the usual ones relying on operators in Hilbert space and path integrals. This formulation is based on Wigner’s function and Weyl’s correspondence between operators in Hilbert space and \(\mathbb{C}\)-number functions in phase-space, endowed with a particular \(*\)-product enforcing noncommutativity. All basic facts regarding the Wigner’s function and its use in the formulation of quantum mechanics are dealt with, including the uncertainty principle, Ehrenfest’s theorem, stationary perturbation theory, propagators and canonical transformations. An interesting historical outline and an extensive list of references close the first part. The second part consists of 23 key selected papers on the subject of phase-space quantization, starting from the milestone papers of Weyl and Wigner to most recent ones, including a review paper.