  We present a complete analytical and numerical solution of the Typical Medium
Theory (TMT) for the Anderson metal-insulator transition. In this theory, we
self-consistently calculate the typical amplitude of the electron wave-We
present a complete analytical and numerical solution of the Typical Medium
Theory (TMT) for the Anderson metal-insulator transition. This approach
self-consistently calculates the typical amplitude of the electronic
wave-functions, thus representing the conceptually simplest order-parameter
theory for the Anderson transition. We identify all possible universality
classes for the critical behavior, which can be found within such a mean-field
approach. This provides insights into how interaction-induced renormalizations
of the disorder potential may produce qualitative modifications of the critical
behavior. We also formulate a simplified description of the leading critical
behavior, thus obtaining an effective Landau theory for Anderson localization.
