When I finished reading the manga of the same name, I had mixed feelings about it; the story was different and definitely thrilling, the art beautiful, but the story progressed slowly.
The anime fixed any problems regarding that.
There is nothing new to the story, compared to manga. The story remains the same, although there are some small pieces missing. A notebook falls from the shinigami world, picked up by Light Yagami - a bored, intelligent young man who seizes this opportunity with minimal hesitation. Write down a person's name and they will die. Get more elaborate, and the death shall follow instructions if possible. Throw in master detective L, and the game is ready to begin.
The art is exceptionally nice to look at.
The pace is just right, the characters' qualities embraced.
For anyone in love with Death Note manga, check this out.