The Reduced Shakespeare Company got their start in 1981, according to their website, "at Renaissance Faires outside of Los Angeles and San Francisco where the entertainment slots allow a maximum performance time of thirty minutes." As a result of this, they learned the style that they still use today: quick jokes, quick transitions, and never for a second letting the audience's attention waver. At this point, the company was Daniel Singer, Jess Borgeson, and Adam Long. Their routine consisted of Hamlet done in twenty minutes, expanded to include Romeo and Juliet in 1983.
In 1987, at the Edinburgh Fringe Festival, The Complete Works of William Shakespeare (abridged) was performed for the first time. Due to the overwhelming popularity of the show, the company began to tour the United States the next year, adding in audience participation and stretching the length of the show. In subsequent years, the show made its way to a number of different countries all across the world.
In 1992, Jess Borgeson left the company, which was subsequently joined by Austin Tichenor, who had attended the University of California in Berkeley with Borgeson and Martin. With his help, the company wrote their second major show, The Complete History of America (abridged). It was followed in 1994 by The Ring Reduced, a half-hour version of Richard Wagner's Ring Cycle, airing on Channel Four in Britain. Because of commitments to his new family, Adam Long stopped being a full-time member that year, and the company was joined by Matt Croke. 1995 saw The Bible: The Complete Word of God (abridged), and The Reduced Shakespeare Company Christmas. In 1998, they were joined by Dee Ryan, who replaced Matt Croke when he decided to take a break.
Since then, the company has written (and performed) The Complete Millennium Musical (abridged) in 1998 (which was later renamed to Western Civilization! The Complete Musical (abridged)) and All the Great Books (abridged) in 2002. They can be seen in London at the Criterion Theatre, in Washington, DC at the Kennedy Center, and in Pittsburgh, Pennsylvania at the Pittsburgh Public Theatre, as well as in dozens of other countries through which they tour. Their shows are never exactly the same, as with all great comedy, but anybody seeing one can be assured of a really great time.
The linchpin of their fame is hands-down The Complete Works of William Shakespeare (abridged), which has been to more places and been seen by more people than I'd care to count. The first act of the show takes the audience through all of the Bard's plays but one, all performed in different styles - as a medley, as a cooking program, in drag, and others. The second act is taken up entirely with (of course) Hamlet, which is performed with much audience participation and even greater speed, and which (at the close of the show) is performed very quickly, extremely quickly, and as a grand finale, extremely quickly in reverse.
Source: http://www.reducedshakespeare.com/ | 
