I was first drawn to the trim size, 4" x 5.5", palm size. I can easily imagine a child clutching this book, enamored of the images. After all, it was published in 1942 so military images were part of every day life.
Perhaps the child had a relative or friend serving in some far away land. Their visit home always an exciting occasion. The child's thoughts of war were filled with glory unless reality came to their door.
America's Navy published by Rand McNally & Company in 1942.
Click images to see them larger.
I have found nothing about the cover illustrator Herbert Rudeen other than a few other samples of his work (here and here).
The interior illustrations, which are quite wonderful, were done by George Moll, or so the title page says. Dig a little deeper online about Moll and you discover he was the head of an ad agency called the George Moll Advertising Agency. The art director was Charles H. Steinbache. If you look up Steinbache's name you'll find a lot of artwork that looks similar to what you see here in this book (here, here, here, and here). I simply don't know who really did the work. Possibly just someone in the art department who never got credit. The agency apparently did a lot of work on non-sport trading cards.
To see photos and read more about "Ace" Lieutenant Edward H. O'Hare who appears on the final page of the book click here, here, and here. O'Hare Airport in Chicago was renamed for Lieutenant O'Hare in 1949. He was shot down in 1943 and listed as missing in action.
UPDATE: Thanks to an anonymous commenter we now have a link to see more illustrations featured at the Northeastern University College of Engineering.