These notes represent the material presented in the first eight of ten lectures at a CBMS Regional Conference which was held in Norman, Oklahoma, in June 1970. The author chose those results which seemed to him representative of their areas both as a technique and flavor. The main topics are affine rings, rings of quotients, group algebras, $W^a$-algebras, polynomial identities and their generalizations. In most of the areas touched upon, much work remains to be done; the results developed are merely beginnings of large areas of research that could, or should, be carried out.