Out of interest what reviews make you uncertain? Looking down the only immediately negative review is by some idiot who would recommend Kitto (what year is this?) and manages to misspell the Iliad (seriously?) and sign off with a pretentious comment.

The book is a good one overseen by phenomenal editors. It also happens to rather general, with a societal/cultural focus more so than discrete historical events. Is that what you want?

Your problem is that you want a one book overview. This isn't necessarily possible, even if you ignore scholarly complexities, because there's a lot of upheaval, mutation and transformation as time goes on.

You might want to take a good look at both the Fontana Ancient History series and the various Routledge books - for particular periods. Overall this is probably one of the best introductions you'll find though.