People have always created sign languages, but the origins of the modern system are thought to be in Spain.
In the early 17th century a Spanish priest named Juan Pablo Bonet was working for a wealthy family which had a number of deaf and hearing impaired people in it, especially the wealthy couple's son. From watching this boy have lessons Bonet was inspired to create a system of signs so that deaf and mute people would be able to use an alphabet and learn to write. He published a book on this in 1620, and its influence was great.
Later in the century, writers from other countries including England and Scotland began to describe a manual alphabet, which people spelled out using joints and other parts of their fingers. This was a further step in creating the sign languages used today.
In the 18th century both Britain and France developed sign alphabets very similar to those in use today.