In astronomy, a syzygy (Greek: "yoked together") is a situation where three bodies are situated along a straight line. The word is usually used in context with the Sun, Earth, and the Moon or a planet, where the latter is in conjunction or opposition. Solar and lunar eclipses are examples of syzygies, but the term is also applied to each instance of new moon or full moon when Sun and Moon are in conjunction or opposition even though they are not exactly on one line with the Earth.
The word is also often loosely used to describe interesting configurations of planets in general. For example, situations when all the planets are on the same side of the sun are sometimes called syzygies, although they are not necessarily found along a straight line.
In mathematics, a syzygy is a relation between the generators of a module. All such relations create what is called the first syzygy module. The relations between generators of the first syzygy module form the second syzygy module. This process can be repeated indefinitely, forming higher-order syzygy modules. See Hilbert's syzygy theorem.
Project Syzygy is an alternate reality game. A summary can be found here .