This works on Github:
## Title
### Place 1
Hello, this is some text to fill in this, [here](#place-2), is a link to the second place.
### Place 2
Place one has the fun times of linking here, but I can also link back [here](#place-1).
### Place's 3: other example
Place one has the fun times of linking here, but I can also link back [here](#places-3-other-example).
Summary of the conversion rules:
- punctuation marks will be dropped
- leading white spaces will be dropped
- upper case will be converted to lower
- spaces between letters will be converted to
-
A good example document with plenty of links and formatting is LivingSocial API Design Guide