What is the Harry Potter Book font?

The closest font to the hand-drawn Harry Potter logo is
Harry P.

You can get the font free here:

Harry P. Font

Founder of  Scriptorium Fonts, Dave Nalle, created the font Valdemar. Which is the official Harry Potter font used for titles and captions on all packaging for action figures, toys, games and novelties.

This is a commercial font and is available here:

Valdemar