I saw this post a couple of days ago and put it in my too hard basket because I needed to watch it again as I had forgotton half the names, then I forgot about it.
So I will try and explain it as best I can and then you will be so totally confused, you'll never ask again
Dean Corso is hired by Boris Baulkin to find and compare the other two copies of The Nine Gates of the Kingdom of Shadow with the copy Baulkin had just purchased from Mr Telfor (the one who comitted suicide in the beginning)
His search starts by asking Liana Telfor if Baulkins book did indeed belong to her husband.
Liana was outraged that her husband sold the book and tries to get it back by any means available throughout the movie until she finally succeeds by stealing from it Deans hotel room. (when he hides it behind the fridge)
His search takes him to Portugal where he questions the original owners of the Telfor/now Baulkin copy, they are book restorers, the Cenzia Bros, here Dean learns of the differences in the nine plates/drawing within the book. 6 are signed by AT (the writer of the book) and 3 are signed LCF (the collaborater that helped AT) Dean is skeptical to find that Lucifer signed those 3 different drawings.
Then his search takes him to the first copy that he can compare, the Fargus copy. (I don't know which country this is)
While studying the 2 books together he finds discrepancies within the 2 copies, so he makes a grid and finds that 6 plates are signed by LCF and 12 by AT.
Fargus is killed and a burnt book is recovered before flying to France. Once looked at Dean discovers that pages were ripped from the book before being burnt.
These pages just happen to be the ones signed LCF.
Next on his list is the Baroness Kessler, but before he can get to look at her copy the Baroness puts two and two together and realises that Mr Corso is working for Baulkin and she throws him out. ( bad friendship between Kessler and Baulkin )
After being attacked by Lianas henchman, Dean then photocopies the different plates and gives them to the Baroness as a peace offering so that he can compare her copy with Baulkins, the last 3 plates/drawings of LCF are found in the Kessler copy. While Dean is comparing them he is hit on the head the Baroness is murdered and the place set on fire, Dean just escapes and finds out when he gets back to the hotel that Baulkins copy has been stolen.
He then goes to St Martin to find Liana and get Baulkins copy back.
Baulkin beats him to it, takes the book and Dean follows him until his car stalls in a running stream.
He finds a postcard that Baulkin sent to Kessler of a castle and asks directions to it, where he finds Baulkin summoning the devil by using the 9 drawings/plates that he now has in his posession.
His mumbo jumbo didn't work and Baulkin dies in the fire.
Dean finds out from the girl (devils helper) that the 9th plate/drawing was a forgery by the Cenzia Bros, so Dean goes back to Portugal, where the missing drawing just happens to fall at his feet.
He then goes back to the castle and is admitted to the Kingdom of Shadow because he figured it all out.
Now if you are not totally confused, ask questions and I'll confuse you further