Over a period of 30 years, J.M.W. Turner taught perspective to the students of the Royal Academy. To aid him in his lectures he produced a portfolio of of striking diagrams, demonstrating the theories of different artists and critics on perspective, which he would hold up for his audience to view. Twice he inadvertantly left the portfolio in the back of a hansom cab, and had to advertise for their return. Executed in red and black watercolour on paper, often incorporating texts and occasionally featuring worked-up architectural details, the perspective drawings have a strikingly modern appearance, closer to the works of the Cubists or the Russian Constructivists than to anything associated with Turner. Long held in the Turner archives at Tate, catalogued by Ruskin, a selection of these extraordinary works is published here for the first time, accompanied by an inclsive and accessible essay by Turner scholar Andrea Fredericksen. Of equal fascination to students of graphic design, architecture and contemporary art as to lovers of Turner, this publication adds a new dimension to our appreciation of Britian's greatest painter.