Re-Animator is based on an H. P. Lovecraft story, which is a good way to start. It's the story of Herbert West (Jeffrey Combs), an offbeat European medical student that comes to America to try and perfect his reanimation serum. He recruits a reluctant local student, Dan Cain (Bruce Abbot), into his plans, but their experiments go awry.
The film is shot with a serious air, but Combs plays the mad scientist to great comedic advantage.
What makes the story better than normal is that there is more to the plot than just zombies running amok. Dan Cain is dating the daughter of the dean of the medical school, and when Dan attempts to tell the Dean about Herbert's experiments, the Dean refuses to believe him and forbids him from seeing his daughter again. Dan also alternates between being horrified by Herbert's experiments and seeing the higher purpose. In the meantime, Herbert antagonizes the lecherous Dr. Hall by denouncing his theories in class. When Hall discovers what Herbet and Dan are doing, he wants their discoveries to himself.
This was a low-budget film that knew how to make the most of its money. Alternating between camp and being twisted and bizarre, the storyline keeps you watching throughout. This is definitely a different flavor of zombie film, well worth investigating.