In a forthcoming book, I give a comprehensive theory of design based on group theory. Whereas the book itself requires an advanced knowledge of group theory, the present series of articles will give the material in an intuitive form, and build up any needed group theory, in tutorial passages. The articles will begin by assuming that the reader has no knowledge of group theory, and we will progressively add more and more group theory in an easy form, until we finally are able to get to quite difficult topics in tensor algebras, and give a group-theoretic analysis of complex buildings such as those of Peter Eisenman, Zaha Hadid, Frank Gehry, Coop Himmelblau, Rem Koolhaas, Daniel Libeskind, Greg Lynn, and Bernard Tschumi. This first article is on a subject of considerable psychological relevance: nested symmetries.