The manual is intended for the training specialists in the area of nanomaterials and nanotechnology. The book describes the main trends of quantum mechanics formalism, including operator algebra, matrix mechanics, and Dirac parenthesis unit. Special attention is paid to approximate quantum-mechanical methods, widely used in quantum chemistry. The book includes the elements of the developing direction of quantum mechanics, namely quantum qubits, which is associated with the design and construction of quantum computers in the future. Specific technique of quantum-mechanical calculations are widely discussed. The book is intended for students and teachers of higher technical universities.