This work is a methodology for the design and analysis of adaptive internal model control schemes with provable guarantees of stability and robustness. Written in a self-contained tutorial fashion, this research monograph brings theoretical advances in the design of robust adaptive systems to the realm of industrial applications. It provides a theoretical basis for analytically justifying some of the reported industrial successes of existing adaptive internal model control schemes, and enables the reader to synthesize adaptive versions of their own favourite robust internal model control scheme by combining it with a robust adaptive law. The net result is that earlier empirical IMC designs can now be systematically robustified or replaced altogether by new designs with assured guarantees of stability and robustness.