H. Beam Piper's first stories set in the parallel worlds of Paratime, including the stories that introduce the Paratime Police and Verkan Vall. This collection includes:

Genesis - The fascinating origins of the advanced technology that allows future Earth inhabitants to journey between parallel universes. This story from H. Beam Piper's popular Paratime series tells of the Martian colonists who settled on Earth hundreds of thousands of years ago.
He Walked Around the Horses - Set in 1809, based on the actual disappearance of English diplomat Benjamin Bathurst in Perleburg, Prussia, during the era of the Napoleonic Wars; he walked around some horses in the courtyard of an inn and was never seen again. Piper describes the event through letters and official documents, and unlike most such tales, he breathes such life into the documents to make it all feel contemporary, clear, and vivid. "He Walked Around the Horses" does not mention Paratime, but the Fortean concept clearly was percolating in Piper's mind. The paratemporal process behind the Bathurst disappearance is discussed in other stories, one of which alludes to Bathurst's own situation. This is a little classic.
Police Operation - This novelette introduces Verkan Vall of the Paratime Police. The story is set in a world-line that may well be ours. A team of a State Policeman and a game-warden are tracking a very dangerous beast that got away from a paratimer, a Venusian nighthound. In this adventure we're given the basic explanation of Paratime and how it works.
Last Enemy - This novella is a fast-paced science-fiction adventure that combines the reality of reincarnation in an advanced civilization; a professional society of assassins; rival political parties based on different theories of reincarnation; an impressive gun-battle inside a country mansion; and the very competent Verkan Vall of the Paratime Police and his sometime wife, the smart, lovely and rather explosive Hadron Dalla.
Time Crime - Again, this novella is a police procedural, but this one has much rich detail about the Paratime-travelling "First Level" civilization and its Paratime Police, and why they're necessary. A very solid story about slavery and different levels of civilization, and anti-slavery. Piper develops some of the scarier ramifications of his concept. In "Time Crime" we see more of the ethical side of Piper's hero Verkan Vall, of his lady Hadron Dalla, and the Paratime Police.
Temple Trouble - Crooked Paratimers masquerade as religious leaders in a vulnerable timeline. Piper's dislike of superstition and false idols comes across strongly.