Over half of the stars we see are actually binary or multiple star systems. These systems are important to astronomers because we can measure the masses of stars by studying the orbital properties of binary stars, and there is no way to measure the mass of stars that are not part of binary star systems.
There are several types of binary systems. Some binaries are more than one type.
Optical doubles are not true binary stars because they are not orbiting each other. They are an illusion caused by a chance alignment of stars. The stars appear very close in the sky but are different distances from Earth. They are actually very far apart. Its like an airplane flying in front of the Moon. It looks as if they are very close, but the Moon is much farther away.
Visual binary stars are true binary star systems because the stars actually orbit each other. Visual binaries are far enough apart that we can see them as two stars. We can resolve a few with the naked eye, but most visual binaries require telescopes to resolve the two stars. To resolve them as two stars, the stars must be far apart, so the orbital periods are decades or centuries long.
To distinguish between an optical double and a visual binary, we must observe the stars to see if they are orbiting each other. If they appear to circle around each, they are a visual binary system, otherwise they are an optical double. Because the orbital periods are long it takes a long time to make these observations.
Telescopes cannot resolve eclipsing binary systems into two stars. We know that they are binary stars because they are lined up in such a way that the stars pass in front of each other during their orbits. When one of the stars is in front of the other star and blocking its light, the star is eclipsing the other. During eclipses, the star appears fainter because we do not see the light from the eclipsed star. Because their brightness varies eclipsing binaries are also a type of variable star.
Telescopes are also unable to resolve spectroscopic binary star systems. We know that they are binary systems because their spectra show two sets of spectral lines - one from each star.
We also see alternating red and blue Doppler shifts in the spectral lines, meaning that the stars are alternating between moving away from us and towards us. While one of the stars is moving towards us, the other is moving away. These observations tell us that the two stars are mutually orbiting each other.
Some spectroscopic binary stars have one star much fainter than the other. In these single lined spectroscopic binaries, we only see one set of spectral lines with alternating blue and red Doppler shifts. We must infer that the other star is there.
Some spectroscopic binary stars are also eclipsing binary stars.
In addition to binary star systems, there are stars systems with three, four, or more stars. These multiple star systems can be any combination of visual, eclipsing, or spectroscopic systems. They are often very complex systems.
Mass is the most important fundamental property of stars. If we know the star's initial mass and composition, we can, in principle, predict the star's entire life cycle. The only way to measure the mass of stars is to study the orbital properties of binary stars. These orbital properties are determined by gravitational force, which is in turn determined by the mass. Applying Newton's laws and Kepler's third law allows us to determine the masses of the stars in a binary system from the orbital properties.
Morrison, D., Wolff, S. and Fraknoi, A., Exploration of the Universe, Saunders, 1995.