Are you sure about the markdown code you've posted?
I believe it's either
Code:
## Chapter 1
This is the first line of chapter one.
## Chapter 2
This is the first line of chapter two.
## Chapter 3
This is the first line of chapter three.
## About the Author
OR
Code:
Chapter 1
-----------
This is the first line of chapter one.
Chapter 2
-----------
This is the first line of chapter two.
Chapter 3
-----------
This is the first line of chapter three.
About the Author
-------------------
In either case things will be mapped to h2's. For h1's usw a single # or an = sign.