RECIPROCAL FRAMES is an introductory book on reciprocal frames related to design science. The book expands my previous article 'The Wooden Roofs of Leonardo and the New Structural Research' already published on the 'Nexus Network Journal' (2008). These structures can be consideraded as forerunners to rigid tensegrity structures, wich can themselves be considered the forerunners to geodesic domes.At its most simple and natural form a design science structure starts as a three-dimensional weaving with reciprocal joint, expanding and oscillating in the space by means of the tensegrity joint and at last it consolidates and simplifies through the punctual joint.This expanded and updated english version of my book STRUTTURE RECIPROCHE E GEOMETRIA SINERGETICA (2009) links to the new topics described in my books listed in the bibliography.