GoodNotes lets you take handwritten notes, sketch diagrams, mark-up PDFs and organize them on a beautiful bookshelf. Turn pages with a swipe, highlight or add notes to any page, and share your notes with anyone. GoodNotes will automatically save your notes and has full backup function to prevent data loss.
RH: This is the free version of GoodNotes. This app provides a number of templates including lined, blank, squares, and music note sheets. The free version limits you to two notebooks and the upgrade is a little pricey at 3.99. I really like the ability to enlarge your paper as you write and then shrink it back at will. You can also import images and be able to write all over them.