Dean Corso (Johnny Depp) is hired to verify that a book owned by Boris Balkan (Frank Langella) is authentic. Boris had bought the book from Andrew Telfer. Balkan wants to use the book to contact the devil, There are 3 copies. Each book is different and Corso figures out that the only way to contact the devil is to use all 3, as each one has a different part. All along Corso is being chased, but keeps getting saved by a nameless woman (Emmanuelle Seigner). She seems to have abnormal powers.
In the end, Balkan had the other owners of the books killed, and he tries to get through the 9th gate. He fails and Corso ends up killing him to end his suffering.
Corso ends up deciphering the last clue, which is a diagram of the mysterious girl who has been helping him. Corso ends up going through the ninth gate. The audience is left hanging, as we don't know where it leads to.
Thanks John R!