[help experience]
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You get experience mostly from killing monsters. You can
also get experience from solving some puzzles, and you'll usually
be told when you've received experience this way. Note that while
you get a little experience for just fighting the monster (1 point
per h.p. of damage you do) you get most of your experience for the
actual kill.
 
You can also buy experience. When you go to the guild to advance,
you have the option of making up any difference between the needed
experience and the experience you have with cash. If you have the
amount of experience you need, then you can advance for free.