H. Beam Piper
This is the classic culmination of the Paratime stories, composed of three short stories that Piper had published in the 60s dealing with Coporal Calvin Morrison, a Pennsylvania policeman who was accidentally transported from his own Earth (basically ours) to one where the Aryan migration went east from India instead of west. His love of military history and his knack for strategy and tactics propel his meteoric rise in the new Earth; the doomed kingdom he fell into becomes a conquerer instead, in a war against a theocracy based on the magic of gunpowder.
Naturally, he knows the secret formula, and quickly gains the trust of the ruling family. This becomes a bit of a headache to the Paratime Police, because they not only have to cover his disappearance on his own time-line, but have to figure out if he's a threat to the Paratime Secret. And they don't want to kill him... unless they have to, of course. Moreover, the university researchers are fascinated, because they can study the massive impact that one person can have on a time-line, using nearby lines as controls.
And as for Calvin, he's having a blast. He gets to be a hero, he gets to put his beloved military theories into practice, he gets to toss off great lines like "And there was the great god Status, whose symbols were many, and who rode in the chariot Cadillac, which was almost a god in itself," and, of course, there's a beautiful princess in it for him as well, and it doesn't hurt that she can outfight half the kingdom.
This is the ultimate book of wish fulfillment. A somewhat ordinary guy from our world gets transported to the one place where he can be truly great. Despite the clichéd premise, though, this is truly a fun read.
(Note; currently this is published with the Paratime stories below as The Complete Paratime. I preferred the Whelan cover, though.)