The source is the documentation!
(General wisdom)
The TYPO3 APIs are first and foremost documented inside of the source scripts. It would be impossible to maintain documentation at more than one location given the fact that things change and sometimes fast.
We have dedicated ourselves to document the classes and methods inside the source scripts (JavaDoc style). This means that you can use any JavaDoc compliant documentor programme to extract API documentation from the source. You can also install the extension "extdeveval" which will offer you a menu with links to the most important APIs in TYPO3 from within TYPO3:
Clicking a link like "extMgm" will bring up a new window with the full API of that class: