This is an
RPG marketed by
TSR and developed by
E. Gary Gygax. While there are many universes designed to fit with this set of rules, the technology is usually vaguely
medieval, and the game generally focuses on wizards using spells and warriors using sharp objects to kill monsters and take gold and magical items, and also gain
experience which enables them to become more powerful. Along the way they tend to do the sort of heroic things you see in fantasy novels.
The first edition of the game, or basic set had a number of problems. A dagger could attack twice per round, doing between one and four hitpoints of damage, while a sword could only attack once per round, doing between one to six hitpoints of damage. A dagger was a better weapon than a sword, especially if you had a good strength bonus!
There are now a number of books of rules, and a number of gaming universes in which these rules can be used, and a number of D&D modules for each universe. In general, creating a D&D character requires somewhat less thought about character conception than some other games such as GURPS, and is somewhat faster, although there is a fair amount of die rolling and paperwork involved. Despite the D&D skills system the characters are somewhat less indivdual than in some other role playing games, but can still be a lot of fun. D&D tends to be many people's introduction to role playing.