What do you mean by "book"? If you mean, have we found texts in general, the answer is a resounding yes. If you mean, have we found any fictional stories, then the answer is also a resounding yes. If you mean have we found any bound books with pages (called codexes a codex [EDIT: singular codex plural codices]), then the answer is also yes.
Here are some of the texts that we have discovered from Ancient Egypt:
My favorite is the The Tale of Sinuhe an Egyptian story with themes of divine providence and mercy. The anonymous author has been called the "Egyptian Shakespeare" if that gives you an idea of its importance, and many copies have been found throughout Egypt, so it was a very popular work in ancient times.
Another well-known fictional tale is The Tale of Wenamun, another Egyptian tale of misadventures abroad.
We have a lot of myths and tales of the gods of Ancient Egypt, such as The Contendings of Horus and Seth, which is actually being made into a Hollywood movie. We have the Legend of Ra and Isis.
We've also found some religious texts that were hymns, such as the Hymn to the Aten.
There are also a lot of scientific texts such as the Edwin Smith Surgical Papyrus.
And these are just a taste. For a much longer list of texts with translations and commentary, check out this website
I can't answer your question directly but I can tell you a little bit about Egyptian literature. There were two types of script in ancient Egypt: the hieroglyphs that most of us are familiar with and another script called Demotic. These are two of the languages inscribed on the famous Rosetta Stone, along with ancient Greek. In fact, by about the time of the Rosetta Stone's creation (196AD), hieroglyphs were typically only read and understood by by priests alone. A lot of hieroglyph texts have survived because they're ceremonially painted on walls of tombs etc. Unfortunately, other Egyptian texts have been lost because they were written on papyrus, which is made of plant fibres.
By book, do you mean a novel? Or just any written text? If it's the second one, there are many examples. Here is a page from the Book of the Dead for example.
