H. Beam Piper
In this collection of short stories set in a world where First Level inhabitants exploit the resources of four other Levels, each with numerous subsections, Piper constructs police narratives in an otherworldly format. In "He Walked Around the Horses," we find out a possible fate for that Charles Fort favorite, Benjamin Bathurst, a man who disappeared in broad daylight from the knowledge of anyone in this world. The story is told through official correspondence on another Earth, a world where the American Revolution failed, affecting events all over Europe. Naturally, the inhabitants of that world think of the sudden appearance of a British diplomat - and one who has a very strange view of current events - as exceptionally distrubing.
The next story deals with trying to clean up after a careless First Level inhabitant, one who brought an alien pet to a lower-level timeline, which escaped after the owner died. In this story, we are introduced to Verkan Vall, future head of the Paratime Police, an organization which keeps track of activity in the other levels, and which is dedicated to preserving the Paratime Secret. In this case, that means tracking down and removing the vicious alien pet before it is seen and killed. In other cases, it means discrediting flying saucers (observation discs) and explaining inexplicable disappearances (such as the unfortunate Benjamin Bathurst.)
There is then a story set on the Second Level, in a culture in which reincarnation is a proven fact of life, and "voluntary disincarnation" is common. The trouble starts with a First Level infiltrator who is innocently carrying out research that has huge sociological implications. Her life is, of course, threatened, and Vall must extract her before her involuntary discarnation takes place... because her reincarnation, along with memory recovery, could give the Paratime Secret away.
The story "Time Crime" is the longest in the book, and the slowest as well, as it is mostly procedural. However, readers will sympathize with the all-too-modern fact of having to deal with the media and with politicians while trying to do your job; these passages with attacks from all sides seem all to familiar in an age where every last bit of information is over-analyzed.
I would recommend this book for people looking for classic science fiction in small doses. These stories are well-written and still hold true, even with the anachronisms.