Abu Ja'far Muhammad ibn Musa AlKhwarizmi was an
Arab
(or
Persian)
geographer,
astronomer, and
mathematician who lived
from about 160230
AH^{1}, at the height of
Abbasid power in
Baghdad.
He is well known because his works, translated into Latin in the
12th century (primarily by Leonardo of Pisa, better known as Fibonacci), became the principal conduit of mathematical knowledge
to the West.
Of principal note is alKitab almukhtasar fi hisab aljabr wa'lmuqabala^{2},
a collection of techniques of symbol manipulation. It is unclear
how many of these techniques he invented himself, and how many he adopted
from earlier (including Indian and Ancient Greek) mathematicians.
From his works arose Western use of

algebra (a corruption of Aljabr),

Indian numbers (called "arabic numbers" in the West) including
a zero, from a work (Algoritmi de numero Indorum^{3})
whose Arabic text is now lost.

Decimal positional notation (known then as algorism or augrim)

As aljabr was a really about strategies for solving mathematical
problems, his name, or rather a corruption of it, "algorithm", became
associated with such strategies.

John Napier may have invented the word logarithm to be parallel with
"algorithm". He never explained where he got the word from; another
mathematician, Henry Briggs, ascribes a Greek origin to the word.
He also published
Kitab surat alard^{4}, a
gazetteer
improving on
Claudius Ptolemy's
Geographia.
^{1}about 780850
AD
^{2}The Compendious Book on Calculation by Completion and Balancing”
^{3}"AlKhwarizmi Concerning the Hindu Art of Reckoning”.
^{4}"The Image of the Earth", or more simply, "
Geography"
Sources:
http://wwwgroups.dcs.standrews.ac.uk/~history/Mathematicians/AlKhwarizmi.html
http://members.tripod.com/~wzzz/KHAWARIZ.html
http://www.britannica.com/eb/article?eu=46427