An absolutely excellent collection of classic SF short stories. I would find it hard to pick a favorite. Arthur C. Clarke's The Nine Billion Names of God is one of the most famous SF stories of all time. The Tibetan monks want to buy a computer that will write out all of God's nine billion names, but what is their real plan? I also love Poul Anderson's The Man Who Came Early, a haunting story of a modern American GI who somehow finds himself back in 10th century Iceland. He finds that it's not as easy as he'd expected to impress people with his superior technology. C.M. Kornbluth's The Mindworm is one of the best telepathy stories ever. And for sheer weirdness, there isn't much to beat Theodore Sturgeon's The Other Celia, where we meet the woman who keeps a perfect replica of herself hidden in her room in a cheap boarding house. Perfect, that is to say, except that there's only the empty skin, with nothing inside.
If you like SF and haven't already come across these gems, do yourself a favor and buy Damon Knight's anthology today. Out of print, but easy to find at abebooks.com...