  Several km-scale gravitational-wave detectors have been constructed world
wide. These instruments combine a number of advanced technologies to push the
limits of precision length measurement. The core devices are laser
interferometers of a new kind; developed from the classical Michelson topology
these interferometers integrate additional optical elements, which
significantly change the properties of the optical system. Much of the design
and analysis of these laser interferometers can be performed using well-known
classical optical techniques; however, the complex optical layouts provide a
new challenge. In this review we give a textbook-style introduction to the
optical science required for the understanding of modern gravitational wave
detectors, as well as other high-precision laser interferometers. In addition,
we provide a number of examples for a freely available interferometer
simulation software and encourage the reader to use these examples to gain
hands-on experience with the discussed optical methods.
