Here you'll find some API documentation of TYPO3 made with doxygen. You can browse them online on this page or download the archives if you want to provide it in your intranet or if you need it online. Please keep in mind, that you'll need a running webserver with PHP if you want to use the integrated search.
Doxygen documentation of core version 4.2 beta2
Doxygen documentation of core version 4.1.2
Doxygen documentation of core version 4.1
Doxygen documentation of core version 4.0.4
Doxygen documentation of core version 4.0
Doxygen documentation of core version 3.8.1
Doxygen documentation of core version 3.8.0