Several km-scale gravitational-wave detectors have been constructed worldwide.
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.