This innovative new textbook contains forty-nine theorems, sixteen corollaries, one criterion, and one law, and thus for the first time, approaches quantum mechanics in a manner to be established on the basis of exact proofs instead of on postulates, principles, axioms, hypotheses, assumptions, and guesses, and in a manner to be free from paradoxes. In this textbook, most chapters start with a bit of history, because the historical experiences are worthy to note. All the difficult points, such as the wave-particle duality and uncertainty relations and operator representation of the observable are proved exactly by mathematics, and thus the concepts and pictures in quantum mechanics become easy to understand and imagine. If readers understand the preparations for analytical mechanics and mathematics in Chapter Two, then they can understand quantum mechanics without a lot of difficulties. This textbook makes quantum mechanics go from covered in a mysterious veil to the uncovered truth. The author would like to predict that there will be a day certainly that this textbook becomes a standard textbook of quantum mechanics in our world.