It is funny how certain things can be suddenly blown way out of proportion. Just look at the rivalry between high-school students Makoto Mizuhara and Katsuhiko Jinnai. Makoto never really meant to be so good at everything, or to best Jinnai in all matters academic, social, and athletic. Of course, Jinnai thought otherwise, and has decided that Makoto is his sworn, bitt'rest enemy. And when Jinnai loses the credit for uncovering a rare archeological find because of his younger sister, who has a crush on Makoto -- well, that was simply the last straw.
So the next night, Jinnai lures Makoto to school after-hours to, um, deal with him. However, a bizarre event interferes in the form of a beautiful woman who tells Makoto that she's been waiting for him, and will transport him to the world of El-Hazard. Before anyone can protest, Makoto, Jinnai, his sister, and hard-drinking, chain-smoking Mr. Fujisawa are whisked away to a magical, mysterious realm full of political intrigue, surprises, and mistaken identity. Things begin to fall apart as the four find themselves as key players in the ultimate struggle for dominance of all of El Hazard!
Synopsis from http://www.themanime.org/