1793 -- Parisian calligrapher Valentin Hauy designed a simplified italic alphabet in embossed print for use by blind people at his the institution he had founded in 1785.

"We ordered typographical characters to be cast of the form in which their impression strikes our eyes, and by applying to these a paper wet, as the printers do, we produced the first exemplar which had till then appeared of letters whose elevation renders them obvious to the origin of a library for the use of the blind."
-- An Essay on the Education of the Blind by Hauy

1837 -- Englishman T.M. Lucas used an alphabet of raised phonetic symbols in a transcription of the New Testament. This was system was improved by James H. Frere who invented the return line, in which the one line reads left to right, and the next reads right to left. This allows a page to be read without lifting your finger.

1825 -- 16 year old Louis Braille, a pupil at the Hauy Institute (remember Hauy? He was the first guy I mentioned) invented the current system witch uses completely new graphemes.
Charles Barber had already made a code for the British army to use, made of a small grid of 12 raised dots for each letter, which had the advantage of being able to be both read and written (with an awl) by it's users. Louis cut it down to just 6 dots per letter. The braille system only came into common usage in 1878 after the International Congress in Paris.

1878 -- An american named J.W. Smith modified the traditional British braille so that the most commonly used letters used the least dots. This became known as American braille.