This text is written for engineers and scientists who have some experience in the field of optics and want to know more about the details and derivations of equations used in optical design. Organized by topic, the book begins with the fundamental law of geometrical optics, Snell's law of refraction, and states the paraxial ray trace equations, then moves on to thin lenses and increasingly more sophisticated components and multi-element systems. Each topic is covered in depth and provides comprehensive information on performance and limitations. While the text is based on general optical laws, special emphasis has been placed on the two major infrared regions - the mid-wave (MWIR) and the long-wave (LWIR). This is particularly important with regard to diffractive hybrids, which have found their place in these long wavelength areas for the correction of chromatic aberrations and athermalization. Comments relating to single-point diamond turning have also been included because this process is predominantly used to produce optical elements for the infrared regions.