(FORTUNE Magazine) - In an industry where so many others are sputtering, Toyota (Research) is a runaway train. It produces nearly 50% more automobiles than it did in 2001, and this year it will almost certainly pass General Motors to become the world's largest car company by volume. In 2005 it earned $11.4 billion--more than all other major automakers combined. Now it has become the first non-U.S. company to break into the top ten on our America's Most Admired list. In a word, and here we paraphrase the unspoken opinion of its competitors, "Yikes!" To find out what Toyota has that the other guys don't, we sent our resident auto maven ALEX TAYLOR III to Japan. He came back with a remarkable tale that shows how this secretive company is changing the world: the untold story of the hybrid car.