EDIT History
Mongols used many alphabets. The script shown here was derived from the Uighur script and instituted as the script for the Mongol language by Chinggis Qagan (Genghis Khan) in 1204.
The Uighur script itself evolved out of Sogdian Aramaic which used to be written left to right until, probably because of influences by chinese writing, its direction got turned around 90 degrees.
Pressure by the Soviet Union led to a law by the Mongolian Peoples Republic (Outer Mongolia) to abolish the Mongolian Alphabet. Before, the Latin alphabet (1931) and the Cyrillic alphabet(1937) had already been adopted for use.
Since the 1990ies, attempts are made to reinstall the use of the Mongolian script in Outer Mongolia.

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EDIT Scripts
The characters in the Mongolian Unicode block are used to write the Mongolian script as well as the related scripts:

Todo (for the Kalmyk dialect of Mongolian), Manchu and Sibe.

They are all in way derived from the Mongolian script, but none of them uses all characters and they each need some extra characters encoded in other areas of the Unicode.

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EDIT Oldest Document
The earliest preserved use is an inscription on a stone stele erected in approximately 1225.

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EDIT Spread
Today, there are about 5-6 million people still using the vertical Mongolian script, mainly in the north of China (Inner Mongolia) where it had not been replaced by a Cyrillic alphabet like in the Mongolian Peoples Republik (Outer Mongolia). There are attempts to revive its use in Outer Mongolia.

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EDIT Writing direction The Mongolian script is written vertically from top to bottom with the lines going from left to right. Vertical Mongolian is a lot more expansive than English, a similar text uses about four times more space when written in Mongolian.
Being a script-alphabet, the handwritten Mongolian finishes each word in one single pen stroke.

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EDIT Characters
There are three different versions of the characters depending on their position (beginning, middle or end of word). The characters also change shape when followed by certain other characters or in specific character combinations.

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EDIT Numbers
(Unicode position U+1810 – U+1819) are assembled vertically as the other characters are. Europen digits can also be used and are rotated 90 degrees clockwise.

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EDIT Currency Symbol
The symbol for the Mongolian currency, Tugrik, can be found under U+20AE as part of the block U+20A0 – U+20CF (Currency Symbols).

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