Lord Kalvan of Otherwhen is H. Beam Piper's last novel, set in his Paratime milieu. A Pennsylvania state trooper is accidentally transported to a parallel, less-advanced Earth.
In another universe, humanity has discovered a second dimension of time that allows them to travel to parallel universes. Being very resource poor, they take a little bit, not enough to be missed, from other universes. The Paratime Police is established to protect their secret. Occasionally, however, unsuspecting people are inadvertently transported elsewhere.
Such is what happens to Pennsylvania State Police Corporal Calvin Morrison, who ends up on an Earth that has 16th century technology, e.g. primitive firearms. While helping to fight off a raid from a neighboring kingdom, he is nearly killed by friendly fire. He falls in love with his beautiful shooter, Princess Rylla, as he recovers from his wound.
Her father, Prince Ptosphes of Hostigos, has defied the powerful priests of Styphon, who alone know how to manufacture gunpowder ("fireseed"). As a result, they refuse to sell him any, leaving him at the mercy of his rival princes. Morrison, called "Lord Kalvan" by the locals, is soon producing a better quality of gunpowder, manufacturing better weapons, and retraining Ptosphes's army in more modern tactics. With these advantages and his leadership, he defeats the numerically superior enemy armies and in the process, founds a new kingdom, with himself as its ruler and Rylla as his queen.
Meanwhile, the new head of the Paratime Police tracks him down and, pretending to be a local trader, becomes his trusted adviser. Having grown fond of Kalvan and being impressed by his accomplishments, he persuades his superiors not to assassinate Kalvan to protect their secret, but rather to let academics watch to see if a great man can single-handedly change the course of history.
Best part of story, including ending:
It's quite entertaining.
Best scene in story:
When Rylla visits the convalescing Morrison for the first time, she mimes her embarrassment at having shot him.
Opinion about the main character:
He's a likable enough character, though he suffers from the standard flaw of this genre. He knows and is good at everything, and rarely if ever makes a mistake.