The 1990 Grainger Lectures delivered at the University of Illinois, Urbana-Champaign, September 28 - October 1, 1990 were devoted to a critical reexamination of the foundations of adaptive control. In this volume the lectures are expanded by most recent developments and solutions for some long-standing open problems. Concepts and approaches presented are both novel and of fundamental importance for adaptive control research in the 1990s. The papers in Part I present unifications, reappraisals and new results on tunability, convergence and robustness of adaptive linear control, whereas the papers in Part II formulate new problems in adaptive control of nonlinear systems and solve them without any linear constraints imposed on the nonlinearities.