This volume collects the proceedings of the International Congress of Studies (Rome, Swiss Institute, 9 October 2006; Urbino, Palazzo Ducale, 10 - 11 October 2006) promoted by the International Center of Studies Urbino e la prospettiva and intended to investigate in its multiple aspects the relationship between the mathematical sciences and the arts, with the contribution of some of the most authoritative experts in the field. The fulcrum of the reflections which emerged from the congress lies in the acknowledgment of the central role played in the history of perspective by the studies carried out in the Renaissance court of the Dukes of Urbino by personages such as Piero della Francesca, Bramante, Raphael, Federigo Commandino and Guidobaldo del Monte. From the second half of the fifteenth century to the first half of the seventeenth century, in fact, the Dukedom of Urbino was at the center of a vast artistic, technical and scientific debate, intended to define the idea of perspective as a rigorous system of representation of reality founded on mathematical bases, and to clarify its possible applications in painting and in architecture. After the empirical studies of Brunelleschi and Masaccio, in 1435 Leon Battista Alberti (many times guest in Urbino of the Duke Federico da Montefeltro) supplied in his De Pictura a first systematic analysis of the idea of perspective and of the perspective-linear method. The merit to have driven the study of perspective along the rails of the scientific codification, however, goes to Piero della Francesca. In his treatise De Prospectiva Pingendi - composed in 1475 and dedicated to Duke Federico - the geometric foundations of the science of perspective are exposed for the first time in a mathematically rigorous way. The effective separation between the study of perspective addressed towards painting and architecture and its purely mathematical formalization has to be attributed instead to Federigo Commandino from Urbino and to his brilliant student Guidobaldo del Monte. The latter published in Pesaro in 1600 his Perspectivae libri sex, an almost exhaustive treatise of the entire discipline which would have opened the road to sectors of our modern mathematics as descriptive geometry and projective geometry, as well as to a wide range of applications in mechanics, architecture, theatrical scenographies and computer graphics. Inspired by these stimuli, the interventions contained in this volume analyze with great thoroughness the history and the applications of perspective in art, architecture and science from the Renaissance to the late seventeenth century, and reflect on the role of mathematics in the study and the most recent developments of the discipline.