The Book of the Week is Dune by Frank Herbert. This is the first hardcover edition, but unfortunately not the first printing. When collectors describe a book as a "first edition," what they really mean is "first edition, first printing." The Book of the Week was not part of the very first print run of Dune in 1965, but instead a later print run (the seventh) in 1966. The cover looks exactly the same as the first printing, and the book is distinguishable from the first printing only in that (i) the price on the inside flap is $7.95 instead of $5.95, (ii) it is bound in red cloth instead of blue, and (iii) the copyright page does not have the words "First Edition" and contains a row of numbers beginning with the number "6," indicating that it was printed in 1966. What's the difference? About $5,000 on the collectors' market.
Because Dune was rejected by every major science fiction book publisher, this first edition of Dune was printed by Chilton, a small publisher best known for its auto repair manuals. As a novice SF publisher, Chilton made the foolish mistake of beginning the book with an 18-page glossary of terms used in the novel. Despite this daunting opening, Dune quickly became a huge commercial success (hence the multiple printings) and won Hugo and Nebula Awards for Best Novel.
The cover of the Book of the Week is by John Schoenherr. This same cover art had already appeared on the cover of the January 1965 issue of Analog magazine, which contained Part I of The Prophet of Dune, the second half of the novel. This was much better than Schoenherr's original Dune artwork, but for some reason Schoenherr was asked to do a new cover for the first paperback edition, next week's Book of the Week.