These are interrelated short stories that deal with time travel, generally referred to as Anderson's "Time Patrol" series. In this series, man achieves time travel many millenia from now. To prevent time travelers from altering the past repeatedly (as is entirely possible in Anderson's universe) evolved men ("Danellians") from even further uptime establish the "Time Patrol." The mission of the Time Patrol is to prevent time travellers from altering the "true" past.
There are some excellent stories in this collection. "Brave To Be A King" is my particular favorite. In this story a time traveller is marooned in ancient Persia in the time of Cyrus the Great and becomes "enmeshed in the local gears." In fact, he becomes Cyrus! But despite being a King, he desperately wants to go home! This is a wonderful story with a gritty realism. Highly recommended.
The only downside to this collection is that you cannot appreciate it one story at a time, because to fully grasp each story you must understand the underlying "Time Patrol" premise. But Anderson takes care of that deftly, because the first story in the collection deals with the recruitment of a 1950s American into the Time Patrol. Not only is this a ripping good story, it does a good job of setting the reader up for the other stories in this collection and in the series. If you like this book, you'll also want to read Anderson's other Time Patrol collections, including "The Time Patrol" and "The Shield of Time."