The Crossroads of Time by Andre Norton

Paperback, 190 pages. 1974 3rd printing by Ace. Some stress lines on the spine. Tight copy. 
 
When Blake Walker foiled a murder attempt on one of his neighbors he somehow found himself drafted into a frantic chase for a dangerous criminal - through the almost infinite levels of alternate Earths.

It was a chase that would take him through level upon level of unknown dangers in search of a ruthless genius who had found our Earth the perfect place to begin his series of conquests.

If Walker succeeded, he would save Earth. If he failed, his homeworld could be enslaved, and he could be trapped on an alien Earth!