It's been a long time since I read Asimov's works, I can't personally link to you every detail or idea to the book counterpart, but the Similarities with the book section of the Wikipedia article of this movie reads (bold text by me):
The final script retained some of Asimov's characters and ideas, though the ideas retained were heavily adapted and the plot of the film is not derived from Asimov's work.
The characters of Dr. Susan Calvin, Dr. Alfred Lanning, and Lawrence Robertson resemble their counterparts in the source material only marginally. For example, in Asimov's work Dr. Calvin is middle aged by the time robots even begin to be widely used and recommends the destruction of over sixty robots when it is discovered that one amongst them is not bound by the first law of robotics. In the film, Calvin is an attractive young woman with a strong faith in the laws of robotics who reacts emotionally when robots are shot or destroyed.
Sonny's attempt to hide in a sea of identical robots is loosely based on a similar scene in "Little Lost Robot". The robot-model designation "NS" was taken from the same story. Sonny's dreams and the final scene resemble similar images in "Robot Dreams", and V.I.K.I.'s motivation is an extrapolation of the Three Laws that Asimov explored in "The Evitable Conflict", "Robots and Empire", "Foundation and Earth" and "... That Thou Art Mindful of Him", as well as several other stories.
The premise of robots turning on their creators—originating in Karel Čapek's play R.U.R., and perpetuated in subsequent robot books and films—appears nowhere in Asimov's writings. In fact, Asimov stated explicitly, in interviews and in introductions to published collections of his robot stories, that he entered the genre to protest what he called the Frankenstein complex—the tendency in popular culture to portray robots as menacing. His story lines often involved roboticists and robot characters battling societal anti-robot prejudices.