International Standard Book Number
The ISBN is used to quickly index and find books. Because there is only one ISBN per book the chance of buying the wrong book is eliminated.
An ISBN looks like this: ISBN 1-55105-083-8.
The ISBN can be checked by the following, simple, algorithm:
Multiply the first number by 10, the second by 9, the third by 8, until you get to multiply by 2. Add up the results of each multiplication, add the check digit, and divide it by 11. If there is no remainder, you have a valid ISBN.
The check digit '10' is written as 'X'. There is no need to add 11 or more, because that wouldn't help for dividing by 11 without a remainder.
Source o' knowledge: http://www.publishing.about.com/
, ISBNs are assigned in "blocks". A large publishing company will own multiple blocks, and will be able to publish as many books as they want.