If you mean a physical part of a book:
* Page: The most common word for a single sheet of paper in a book.
* Leaf: A single sheet of paper, often used to refer to two pages together.
* Chapter: A major section of a book, usually with its own title.
* Section: A smaller division within a chapter.
* Paragraph: A group of sentences that deals with a single idea.
* Sentence: A group of words that express a complete thought.
If you mean a part of the content of a book:
* Passage: A short extract of text.
* Excerpt: A longer piece of text taken from the book.
* Quote: A specific phrase or sentence from the book.
* Theme: The main idea or message of the book.
* Plot: The sequence of events in the book.
* Character: A person or creature in the book.
If you mean a smaller part of the book in a more abstract sense:
* Fragment: A small part of the book, often incomplete.
* Bit: A small portion of the book.
* Part: A section of the book, without specifying its size.
Please clarify what you mean by "piece of book" and I can give you a more specific answer.