This should be a good book, but disappoints in both the quantity and quality of its coverage of the great power rivalry for the dominance of space.
It starts well, with an first-person account by Sergei Kruschchev of the first Sputniks. Kruschchev had a unique vantage point on the whole affair, as a technically knowledgeable person with an insider's pass on the political affairs of the Soviet Union. The first chapter or so, on the WW II German effort is worthwhile as well.
From that point it deteriorates rapidly into superficial re-hashes of old news, poorly presented. I started working on an errata, but gave up after averaging one a page for twenty pages. Some are slipups on minor facts: page 159 map referring to "Kennedy Space Flight Center", or using the acronym "LEM", which was discarded in the early 60's, or saying that the Cape was scorpion infested. Some are bad editing, leading to incorrect statements: p. 249 "Mir, which remained in orbit between 1971 and 2001". Some are failures to globally edit, e.g. telling the tale of the renaming of Cape Canaveral twice. There's also a problem of scope: at times it can't decide if it wants to be about the 50s and 60s or today. This on top of being full of technical groaners too numerous to count, like constantly calling RP-1 "volatile" or completely missing the point on why Gemini used ejection seats rather than an escape tower.
A single volume account of the most turbulent days of the space effort would be welcome; sadly, this isn't it. I wish I could even recommend it as an introduction, to be followed immediately by something more in-depth, but it's so full of inaccuracies I would be doing the reader a disservice. For the interested reader, "Apollo" by Murray and Cox, and "Red Star in Orbit" by James Oberg will readably take you through the two sides, are much more thorough and technically correct, and both rated 5 stars by hordes of readers. They will take you three times as long to read, but you will ultimately profit by not having to unlearn any thing later.