An interesting game of cat and mouse
I have both of these on DVD, and watched both a few years back.The two movies shouldn't be thought of as two separate movies but rather as parts 1 and 2. To watch both you will need a little over four hours, it is worth it.The movie is about a brilliant university student (named "Light") who resents the crime and corruption. He happens to find a notebook on the street with the title of "Death Note". This results in his life undergoing a drastic change as the instructions in the notebook claim that, if a human's name is written within it, that person will die of a heart attack with 40 seconds unless written otherwise.
Light tests the authenticity of the book by experimenting with it and killing two local criminals. Now that the books has been confirmed as real he then seeks to become the dispenser of justice by killing the criminals that have escaped the law.

It doesn't take long for Light to realize that L will be his greatest nemesis, and a race to prove mental superiority between the two begins.