it's about arno dorian. his father was an assassin who was assassinated by shay cormac from rogue. Arno then grew up with his friend (elise de la serre) and her templar family. Then elise's father got killed by other templars who opposed him (her father was a templar grand master who wanted peace with the assassins, and some other templars don't want this)
arno was accused of his murder and got thrown to the bastille, where he met his father's (biological father btw) friend pierre bellec (an assassin), and he got inducted to the assassin brotherhood.
arno felt that elise's father's death was his fault (because he was late to send a letter of warning from his stepfather's templar ally), so he set out to find out and assassinate the people behind his murder.
oh yes, arno and elise developed a love interest. and he assassinated bellec because he killed the assassin mentor (?) because he don't want peace between the assassins and templars (the mentor wanted that, so bellec killed him)
long story short, arno found the leader of the templar faction who killed elise's father. in the end elise got killed, the templar is dead, and arno secured the sword of eden that the templar used.
it's very oversimplified, but that's most of the story. correct me if I'm wrong :D