The technical documentation of the Solarus engine’s C++ code is available online, as well as the Solarus Lua scripting API reference.
If you intend to create a game using the Solarus engine or to modify an existing one, you will be interested in the Lua API reference and the format of quest files. The documentation of the C++ classes is only useful if you want to modify the engine.
Stable version (Solarus 1.3)
Solarus 1.3 is the latest version of the engine.
The Lua API allows you to customize almost everything, including the title screen, the pause menu, the dialog box, the HUD and some map entities. It is fully documented. If you want to make your own game, you should use the latest stable version.