Mod 11 and the X character
ISBN-10 weights the digits 10, 9, 8 and so on down to 1, then checks the sum against 11. The larger modulus is what lets it catch transpositions that a mod 10 scheme lets through.
The cost is that one of the eleven possible remainders needs two characters. X is reserved for it, and it only ever appears in the final position.
Hyphens
Hyphens in an ISBN separate the registration group, registrant, and publication elements. They are stripped before the check runs, so 0-306-40615-2 and 0306406152 produce the same verdict.
Every ISBN-10 has an ISBN-13 equivalent that starts with the 978 prefix, and the two carry different check characters. Confirm which one a catalog expects before importing a list.