Exner’s classic monograph describes the basic optical mechanisms in operation in compound eyes and, despite the passage of time, still remains a definitive work. Although his findings were seriously questioned during the modern revival of interest in compound eyes, all his major discoveries have now been validated. The principle of the lens cylinder and the elucidation of the mechanics of apposition and superposition optics are amongst his outstanding contributions. It also includes a broad survey of the optics and anatomy of the eyes of many insect and crustacean species, and the first explanation for the phenomena of pseudopupils and eyeglow. It has been faithfully translated from the original with annotations to aid the reader. The new edition, with a foreword by the late Karl von Frisch, also includes a concise illustrated appendix summarizing present knowledge of optical mechanisms in compound eyes and a useful bibliography.