The aim of the VCMI project is to rewrite the entire Heroes III engine
(VCMI is NOT another mod) giving it new possibilities. Years of
intensive work resulted in creating application with impressive amount
of features. Among the current features are:

- Complete gameplay mechanics
- Almost all objects, abilities, spells and other content
- Basic battle AI and adventure AI
- Many GUI improvements: high resolutions, stack queue, creature window
- Advanced and easy mod support: add new towns, creatures, heroes,
  artifacts and spells without limits or conflicts
- Launcher for easy configuration: download mods from the server and
  install them immediatelly!
- Random map generator that supports objects added by mods

NOTE!
You need the original game data to use this, and most likely you will
need innoextract (available at SBo), in order to unpack it from the exe.
As an example, for the GOG edition of HOMM3, do this as a regular user:

$ vcmibuilder --gog /path/to/setup_homm3_complete_2.0.0.16.exe
$ vcmibuilder --convertMP3

Alternatively, you may try VCMI with the Heroes III Demo game data,
available at SBo as 'homm3_shareware_data'. It is installed system-wide,
so you can always use the full game data in your $HOME folder.