My initial aim was to introduce the powerful but relatively under-used techniques of multichannel quantum defect theory (MQDT) to graduate students in atomic and molecular physics. The methods are particularly attractive in two ways. They provide an elegant, computationally tractable approach to the treatment of molecular Rydberg states, which invalidate the normal molecular assumption that the electronic motion is overwhelmingly rapid compared with other degrees of freedom. In addition the theory offers a unified description of the discrete molecular states below an ionization limit and those above in the ionization continuum. At the same time the novelty of the MQDT method makes it essential to point to the links with the familiar techniques of ‘normal’ molecular physics.

While writing, I realized that workers in two other fields would benefit from a more general treatment of molecular Rydberg states. In the first place there is a huge literature on electronic structure theory or ‘quantum chemistry’, which can, however, handle only the very lowest Rydberg states, owing to the very long range of the excited orbitals. A chapter has been written to show how the familiar quantum chemical techniques can be adapted to handle arbitrary members of the infinite Rydberg series. Secondly, to meet the demands of modern experiments, the chapters involving interaction with radiation take account of developments in the theoretical description of coherent multiphoton excitation and resonant multiphoton ionization.