The new edition of the first volume of Cohen-Tannoudji's groundbreaking textbook introduces the fundamental concepts of quantum mechanics such as waves, particles and probability before explaining the postulates of quantum mechanics in details. In the proven didactic manner the textbook then covers the classical scope of introductory quantum mechanics, namely simple two-level systems, the one-dimensional harmonic oscillator, the quantized angular momentum and particles in a central potential. The entire book has been completely revised to take into account new developments in quantum mechanics curricula. The textbook retains the typical Cohen-Tannoudji style also in the new edition: it explains the fundamental concepts in chapters which are elaborated in accompanying complements that provide more detailed discussions, examples and applications.