The most populated family has been developed and derived from the French Sign Language (LSF) which is very developed since several centuries, and has been also the historic base for the American Sign Language (ASL) subfamily.
Many sign languages are borrowing signs from these two base sign languages, which have their own distinctive vocabulary and syntaxic features, independant of the spoken language where they coexist (with words or fragments of sentences to be read visually on lips, taken from a simplified version of the spoken language, and that complement the more descriptive gestual language carrying some ideographic traits).
However, a quite large number of isolate deaf sign languages are also found around the world (and official in several countries).
Note that for the same oral language, there may also be very different sign languages used, depending on the region where they are used: they also often use their own signed alphabet for spelling untranslatable terms that they borrow or abbreviate from the dominant local spoken language, and that they use in combination with their normal semantic signs. For this reason, deaf sign languages are not strictly following the same classification as spoken or written languages.