This was the first book of Asimov's that I read, and I think it give you a good grasp of what the late great writer's thought was like. You have some of the best short stories included, especially "Nightfall", one of the all-time SF classics, and some enduring favorites of mine, such as "Belief" (which asks what happens when a physicists finds out he can fly)and "Breeds There a Man?" (a rather unsettling tale about mankind's origins and future).
Asimov is at his best form with the short story (the famous Foundation Trilogy began as short stories), and these are the pick of the litter. I'm not sure how many people are aware of Asimov's interests in science history, and he has many delightful essays giving one a window into some of the lesser-known characters in scientific history, and some of Asimov's thoughts on the role of science. Of particular note is also his thesis that technology made slavery obsolete.