Yamibo: Darkness, the Hat & the Travelers of the Books

This Japanese anime series chronicles the incredible journey of Hazuki through many fantasy worlds in search of her one true love. Hazuki is a high school girl who lives with her adopted older sister, Hatsumi. Even though they've always had a very close relationship since childhood, Hazuki has become increasingly tormented by the forbidden love she harbors for Hatsumi beyond sisterly affection. On the night of Hatsumi's sixteenth birthday, when Hazuki tries to steal a kiss from her sleeping sister in a moment of weakness, Hatsumi's body suddenly vanishes in a blinding flash of light. A cuddly talking parakeet, however, soon appears and leads the grieving Hazuki out of the world she has lived in and into a magical library which contains all the worlds in the universe each within a book. The caretaker of the library is an adorable blonde girl named Lilith who has the ability to travel between different book worlds. She becomes Hazuki's travel companion on her quest to search for Hatsumi through many worlds from the stone age to the outer space, and countless ones in between.