This is a review of the 1982 paperback edition, where the title was shortened to just Top Dog. You can find about three editions of this at the Internet Archive. I just picked this one at random.
Normon Thelwell was best known for his cartoons of horses and ponies, but he poked fun of a wide variety of subjects, including life with dogs. Unfortunately, so has just about every other cartoonist, so this collection suffers from comparison.
Are there funny cartoons here? Yes. Are there cartoons that go over subjects that every other cartoonist does? Yes ... although Thelwell sometimes puts a surprising twist on the predictable. When showing a picture of a typical lapdog, a cartoonist usually draws a St. Bernard on someone's lap. The twist here is that guy being sat on ... is smiling.
The basic set up, like that of many of his horse books, is of a how-to guide for owning a dog. The deadpan text often is in direct contrast with the image. Some are more successful than others.
This book was written for a UK audience in the 1960s. American audiences of a certain age will certainly understand some of the jokes, but others may be a puzzle. That weird thing the kid is holding on pages 64 -65 is a carpet beater, because (believe it or not), rugs used to be regularly removed from the home, taken outside and pounded like a drum to remove the worst of the dirt. They weren't just funny looking collectibles on eBay.
Also, in the 1960s, brushing your dog's teeth was thought to be comedy gold. Now, we realize that it's essential for a dog's good health. Docking tails were also common -- now it's illegal in the UK. So, there's a bit of a generation gap to this.
It's a decent enough book, filled with Thelwell's quirky style (which can be amazingly detailed at times, such as the destruction caused by the aforementioned lapdog) but it's nowhere near as funny as many of his other books.