Originally published in 1928 as number twenty-five in the Cambridge Tracts in Mathematics and Mathematical Physics series, and here reissued in its 1958 reprinted form, this book deals with the physical and mathematical aspects of the symmetrical optical system. Steward's explanation is taken in part from lectures delivered to students of mathematics and physics at the University of Cambridge in the early twentieth century. This tract will be of value to anyone with an interest in the history of mathematics or physics.