This textbook presents problems with detailed solutions showing how to apply quantum theory to modern physics. The text is divided in three parts, the first dealing with elementary particles, nuclei and atoms, the second presents quantum entanglement and measurement. Finally complex systems are examinated in depth. The aim of the text is to guide the student towards applying quantum mechanics to research problems. Advanced undergraduates and graduate students will find a rich and challenging source for improving their skills. This new edition has been extended with sections on neutrino oscillations, quantized vortices in Bose-Einstein condensates, quantum correlations in multi-particle systems, Bloch oscillations in periodic lattices and non-destructive quantum measurements.