Use of this unique book will permit correction of the present defect in quantum education throughout the world. The new breakthrough in quantum mechanics was recently achieved due to the inverse problem approach. It allows finding infinite (!) number of exactly solvable models instead of only about ten previously known. It means an incomparable more convenient basis for the quantum education and countless instructive examples of the precise control of the spectral parameters. That was impossible to imagine in the previous quantum theory. Another great achievement was the discovery of qualitative rules of transformations of the most elementary wave constituents, their separate bumps. This opened the 'black box' of the above mentioned exact models and intensifies many times their usefulness. One acquires the notion about the simplest "bricks" and building blocks of potential and wave transformations. It means a real quantum ABC to acquire the quantum literacy and facilitate the future discoveries. So, one gains the absolutely unexpected ability of immediate prediction how, in principle, to achieve the given properties of the constructed objects. An unprecedented combination of qualitative simplicity and clarity with absolute exactness was achieved. Unlike the numerous books on quantum mechanics, mainly compilations, this one has no analogues. Being first hand information it is utmost intelligible due to computer visualisations. It is not a substitution of the traditional books, but a fundamental, strengthening and simplifying addition to them enlarging and deepening the understanding of the subject instead of previously unintuitive and approximate approach.