Along with the traditional material covered in a quantum mechanics course (states, operators, Schrödinger's equation, the hydrogen atom), the book offers in-depth discussions of concepts such as Hilbert space, quantum measurement, entanglement, and decoherence. These concepts are critical to understanding quantum physics and its connection to the macroscopic world, but are rarely covered in entry-level textbooks. The book uses a mathematically simple physical system—photon polarization—as a visualization tool, allowing the student to see the intricate beauty of the quantum world from the very beginning. first pages. Formal concepts of quantum physics are illustrated with examples from modern experimental research such as quantum computers, communications, teleportation, and nonlocality. The book's material has been successfully used as the main teaching tool in a two-semester course in quantum mechanics for undergraduate physics students. However, the potential readership is much wider and includes both undergraduate and graduate students studying exact sciences, as well as anyone interested in quantum physics and quantum technologies. The mathematical apparatus required to understand the book does not go beyond the course of a technical university or mathematical school. The author, a professor at Oxford University, a world-renowned experimenter in the field of quantum optics and quantum information, applies Socratic pedagogy: the student is invited to independently develop the apparatus of quantum physics through sequential solving carefully designed problems. Detailed solutions are presented in the second volume of the manual.