Non perturbative theoretical and practical numerical techniques are developed and applied to studies of the quantum structure and dynamics of highly excited atoms in external fields. Specifically considered are the dynamics of Rydberg atoms in a circularly polarized microwave field and the diamagnetic and resonance structure in static magnetic fields. The methods used include the use of a quasi-energy formalism, coupled to the Lanczos and/or artificial intelligence algorithm using discrete variable representations, fast Fourier transform methods and complex scaling.
