Zangband is one of the most popular Angband variants. Like its predecessor it's a roguelike game (explore dungeons, battle hordes of monsters, gather loot and develop your character).
Though based on the Angband source code (and thus with some similarities in gameplay), Zangband features a lot of additional content and game balance modifications: several dungeons linked by a world map instead of only one dungeon, quests, a different combat system (inspired by Oangband, another Angband variant), more magic schools and spells, different character classes and a lot of new monsters and uniques.
Zangband is heavily inspired by the Amber saga by Roger Zelazny (hence the name, Zelazny Angband) and features a number of creatures, items and uniques from the books. It was first developed by Topi Ylinen, but has seen maintained and modified by several contributors over the years, and is still in development.