This textbook provides a thorough, systematic and comprehensive introduction to quantum physics, covering the fundamental topics such as the wave-particle duality, the uncertainty principle, the Schrodinger equation, single particles under the influence of potentials, the harmonic oscillator, the hydrogen atom, the spin degree of freedom and the Pauli principle. The last part of the book is devoted to advanced topics such as the chemical bonding in molecules, the structure of matter in the solid state and the interaction of light and matter. The book's main aim is fostering the understanding and application of the quantum-mechanical principles without an over-emphasis of the mathematical formalism. This particular didactic approach is apparent also in the extensive supplementary material which focuses on problem-solving skills and providing online material with electronic multiple-choice self-examination questions, a computer lab with Mathematica, and sample tests containing problems and questions from actual exams.