The book gives an introduction to Weyl non-regular quantization suitable for the description of physically interesting quantum systems, where the traditional Dirac-Heisenberg quantization is not applicable. The latter implicitly assumes that the canonical variables describe observables, entailing necessarily the regularity of their exponentials (Weyl operators). However, in physically interesting cases - typically in the presence of a gauge symmetry - non-observable canonical variables are introduced for the description of the states, namely of the relevant representations of the...