This volume contains nine contributions, from leading scientists, which embrace the fundamentals of various aspects of the conceptual development of quantum chemistry. Topics dealt with include the behaviour of molecules in magnetic fields, the long-standing problem of the decoupling of nuclear from electron motion in molecules, the status of density functional theory, and the string model of chemical reactions. Insights into basic concepts are also presented, such as the nature of chemical bonding and molecular structure and the quantum mechanical problem of the phase space. Trends in the mathematical base of quantum chemistry, such as the methods of hyperspherical harmonics and of the wavelet transform are discussed. This work should be useful for researchers and graduate students of quantum and theoretical chemistry, quantum mechanics and chemical physics.