A Brief History of Time or A Briefer History of Time?

Both are correct, however, the second book is obviously a follow up to the first, in this case - or the second in a series.

Two different books.
From Scientific American
Hawking's A Brief History of Time, published in 1988, was a surprise best-seller but a tough read for most people who tackled it. Hawking received many requests for a version that would make his discussion of deep questions about the universe more accessible. This book does that. Hawking and Mlodinow, a physicist turned science writer, proceed by small and careful steps from the early history of astronomy to today's efforts to construct a grand unified theory of the universe.

Thanks, O, I did not know there was second, easier to read, version of the original. I've read the original, sometime only getting through a single page in an hour and I LIKE the subject of Cosmology.

Joe(Hawking is deep)Nation

I am also sure that that they didn't want to publish it as "The Dumbed Down Version."

Joe(especially for Americans)Nation

You could get a copy of 'The Big Dummy's Guide to Time'.