  Canonical quantization relies on Cartesian, canonical, phase-space
coordinates to promote to Hermitian operators, which also become the principal
ingredients in the quantum Hamiltonian. While generally appropriate, this
procedure can also fail, e.g., for covariant, quartic, scalar fields in
five-and-more spacetime dimensions (and possibly four spacetime dimensions as
well), which become trivial; such failures are normally blamed on the `problem'
rather than on the 'quantization procedure'. In Enhanced Quantization the
association of $c$-numbers to $q$-numbers is chosen very differently such that:
(i) there is no need to seek classical, Cartesian, phase-space coordinates;
(ii) every classical, contact transformation is applicable and no change of the
quantum operators arises; (iii) a new understanding of the importance of
'Cartesian coordinates' is established; and (iv) although discussed elsewhere
in detail, the procedures of enhanced quantization offer fully acceptable
solutions yielding non-trivial results for quartic scalar fields in
four-and-more spacetime dimensions. In early sections, this paper offers a
wide-audience approach to the basic principles of Enhanced Quantization using
simple examples; later, several significant examples are cited for a deeper
understanding. An historical note concludes the paper.
