This collection of short stories has a major problem. All stories which feature travel into the past have this problem, and these, which have it to a very large degree, it being the core of the fictional world Anderson has built, have it in spades. That is, it doesn't deal very well with paradox. Sure, paradox is something that the characters worry a lot about, but in the end they mostly ignore it, and go ahead and create the "causal loops" that they worry so much about, and apparently get away with it every time, which is Quite Irritating.
Other than that, they're mostly "OK", but only "OK". There's only one story that particularly stands out as being very good ("The Sorrow of Odin the Goth"), and none that stand out as being very bad. At their best, these stories contain sympathetic, believable characters who struggle with internal conflicts between what they must do, what they want to do, and what is right; at their worst they are entirely predictable and would only serve as a brief diversion to read once and then forget, with all of the characters' casual breaking of the fundamental rules of their organisation forgiven. To his credit, Anderson generally portrays the cultures of the past sympathetically, with even Evil Conquistadores being shown to be people with motivations and not just thoughtless automatons that merely hack and slash and burn - they do evil because they think it's for a greater good, not just for kicks and greed.
Anderson wrote eleven stories set in this world, of which nine are collected here. A later edition with a slightly different name (Time Patrol, without the leading The) apparently includes one more story, so you may prefer to buy that instead. And there is one other book-length story (The Shield Of Time) published seperately. However, on the strength of this book, I have no particular desire to buy either of 'em.