This book deals with the concepts and techniques that have been developed to meet this challenge and with their application to the interpretation of experiment. The author surveys in detail the many-body techniques, scaling, renormalization group, Fermi liquid and Bethe ansatz, which lead to a solution of the Kondo problem for most of the theoretical models. The book also deals with special techniques for N-fold degenerate models for rare earth magnetic impurities. The many-body techniques developed to deal with strong correlation impurity problems have also been extended to provide a partial explanation of heavy fermion behavior.