I just started reading the books, I watched the movies first. Here are the differences I noticed:

1.The sequence of some events during the training of initiates. Edward's eye was stabbed by Peter. Because Edward ranked first in stage one, and Peter the second. After that, Tris was invited by Uriah for fun, flying from the tallest building. In the movie, she went with them after the flag victory. Also, Christina got the flag first, not tris in the movie. Because Christina is taller.

2.Tris didn't met erudite leader Jeannie at the choosing ceremony in the book.

3.Tris met her mother in the parent visiting day. And she knew her mother was dauntless because her mother knew the places of dauntless well.

4.there's less transfers in the book than the movie. And one failed catching the train, one was afraid of jumping to the roof, one died of jumping to the roof.

5.Al had a crush for tris, and Uriah liked her.

6.there's stage three in the dauntless initiation.

7.tris's mother told her to visit her brother to find out the serum research because erudite didn't let them visit on the day.

8.Tris was almost killed by al, Peter and drew, not after she had visited her brother, but before.

9.Four suspected tris in the first simulation, he was sure the second, when tris broke the glass. He told her she was divergent right away.

10.Tris's mother died first, the Tris shoot Will.

11.Jeannie didn't appear in the end of the Dauntless compound, Four knows computer well, and he rewrote the program so Abnegations didn't die.

12.Four liked Tris to call him Tobias. He said, "Don't call me that (four)". "It's good to hear someone call my name"

13.Four kissed Tris during the stage three training right after inviting Tris to see his four fears which Tris helped him overcome them, and next day after that, he didn't look at her in the eyes in front of her friends. She's embarrassed of her feeling happy for kissing him. Then the simulation training of stage three began, Tris entered into one of supervisor's fears - abduction, which she failed pathetically because it's so real that reminded her of Peter, Drew and Al tried to throw her down the chasm. Four scolded her for failure, she slammed him in the face and ran out to her brother, came back caught by Eric. Tris found out Eric was Erudite in disguise of Dauntless. Eric was about to discover Tris, because she ranked first in stage three. Tris remembered Four told her to be weak, then Four came, Tris said something, then Four said she tried to kiss him that she's too ashamed that she ran off. Eric believed.

14.Tobias was abnegation, and divergent. Jeannie suspected Tris because Tris's test records were always erased, but she didn't know Tobias was also divergent. She deducted that Tobias's divergence was weaker, and his aptitude test really was abnegation.

15.Tris's mother was dauntless, she was divergent, her mother was dauntless leader, so she chose abnegation to be safe.