This is a companion volume to the textbook Quantum Mechanics: A Fundamental Approach by the author. The manual starts with simple mathematical and physical terms before moving on to more complex concepts, which are developed gradually but in detail. It contains more than 240 exercises and problems listed at the end of the chapters in Quantum Mechanics and presents full solutions to all these exercises and problems, which are designed to help the reader master the material in the primary text. This mastery will contribute greatly to understanding the concepts and formalism of quantum mechanics, including probability theory for discrete and continuous variables, three-dimensional real vectors, symmetric and selfadjoint vectors, operators in a Hilbert space, operations on vectors, N-dimensional complex vector spaces, direct sums and tensor products of Hilbert spaces and operators, canonical quantisation, time evolution, pure and mixed states, many-particle systems, harmonic and isotropic oscillators, angular momenta, and particles in a static magnetic field, among others.