Formal:
* Section
* Part
* Division
* Segment
* Episode (for a story or history)
* Period (for a historical period)
* Stage (for a development process)
Informal:
* Piece
* Bit
* Part
* Section
* Phase (for a part of a process)
For books:
* Book (if a book is divided into chapters)
* Part (if a book is divided into parts)
* Volume (if a book is in multiple volumes)
The best synonym will depend on the specific context. For example, "chapter" is often used for a part of a book, while "episode" might be more appropriate for a part of a TV show or a historical event.