

Name used by its users (Endonym): American Sign Language, ASL; fingerspelled as:

Native users/signers (estimated): 730,000 1
Total users/signers, including second-language (estimated): 860,000 1
The number of ASL users is difficult to estimate with accuracy. The figure 500,000 has often been quoted for American ASL users, but this appears to come from a single study dating to the 1970s. On the other hand, a 2022 study reported sign language use in 2.8% of American adults, which would translate to 7 million (though these are not all necessarily users of ASL, or fluent in sign language.)2
Where it’s used: ASL is the predominant sign language used by Deaf communities in North America, specifically the United States and mostly English-speaking parts of Canada. It is officially recognized by the Canadian federal government as well as 45 US states and the District of Columbia.
Beyond North America, there are many other countries whose sign languages are based on ASL, sharing significant amounts of vocabulary and/or grammatical structure. Because each nation or region can develop its own standards for sign languages, these commonly develop by incorporating local sign vocabulary into the structure of one (or more) older existing established sign languages. As a result, it is not always clear whether a given language that is similar to ASL should be considered a variant or dialect, rather than a separate language.
The family of languages derived largely or in part from ASL is spread over a wide geographic range, including: Latin America and the Caribbean (Bolivia, Costa Rica, Panama, Belize, Dominican Republic, Puerto Rico, Haiti, Jamaica); West Africa (Senegal, Mali, Ivory Coast, Burkina Faso, Togo, Benin, Nigeria, Ghana, Sierra Leone and others); and Southeast Asia (Malaysia, Indonesia, Singapore, Thailand, and the Philippines).
Furthermore, even where ASL may not be the dominant language it is widely learned as a second language, due to its usefulness as a lingua franca throughout the deaf world (…perhaps, to tweak the Latin phrase, a lingua signa franca?)

Language family and related languages: ASL is most closely related to French Sign Language (LSF) for historical reasons. It was created and standardized at The American School for the Deaf, founded in Hartford, Connecticut by Thomas Gallaudet in 1817. He had traveled to Europe to study systems of communication for the deaf, going first to London but there meeting instructors of French Sign Language who persuaded him to learn the Parisian methods. Gallaudet returned to the US with Laurent Clerc, who taught the Hartford students using a mixture of French Sign Language alongside home-grown American sign languages that some of the students had brought to the school with them. Graduates continued to teach the language they had learned, many establishing schools for the deaf across other parts of the US, thus spreading ASL throughout the country. Today, it is estimated that nearly 60% of modern ASL signs are cognate to Old French Sign Language. In turn, ASL has gone on to be highly influential to many other sign languages of the world due to its introduction by missionaries, educators, and other advocates within local Deaf communities. Quebec Sign Language (LSQ), the predominant sign language of Francophone Canada, is closely related to both French Sign Language and to ASL.
A small number of words and concepts have been borrowed from English into ASL, for instance some compound and fingerspelled words, though it is important to recognize that ASL is a unique language with its own vocabulary, structure, and grammar distinct from English or any other spoken language.
In contrast, systems of Signed English or Manually Coded English are distinct from ASL. They may derive most of their sign vocabulary from ASL, but follow the grammatical structure of spoken or written English, either partially or exactly. Proponents of Signed English methods have felt that they facilitate mainstreaming of deaf students to English; however they have not generally been embraced or naturally used by the majority of the Deaf community.
Many other sign languages exist throughout the world which are neither similar to nor derived from ASL. In particular, the sign languages used in the United Kingdom (British Sign Language), Australia (Auslan), and New Zealand (NZSL) are related to one another but not at all mutually intelligible with ASL. Another family of closely related sign languages are known as Hand Talk, which was used by many indigenous nations of North America not only by deaf individuals, but as a second language to communicate with speakers of different oral languages. Hand Talk developed well prior to European contact, and in fact many believe it to be one of the several sources that contributed to modern ASL.
NOTES
1Ethnologue. (25th ed., 2022).
2Mitchell, Ross E. “How Many People Use Sign Language? A National Health Survey-Based Estimate.” J Deaf Stud Deaf Educ. 2022 Dec 23;28(1):1-6.