What type of audience did William shakespeare write for?

A very broad audience. The outdoor public theatres attracted people from the lower and middle classes, and the theatre companies were often called upon to perform the same plays in private performances for the aristocracy and royalty. The plays therefore needed to have something for everyone, because nearly everyone went to see them. Dirty jokes and action scenes pleased the groundlings (who Hamlet, ever a snob, said liked only "inexplicable dumb-shows and noise"), the romances pleased the bourgeois and the wit and intellectual points pleased the nobility and royalty.

As Shakespeare's career went on, the theatre companies focussed more on the indoor theatres, which had smaller audiences but bigger ticket prices. Taking the groundlings out of the equation meant that playwrights started writing more for the upper and middle class clientele, and less for the groundlings.