Anthem is more of a short story or fable than a book; think of it as a very condensed Atlas Shrugged if you like. Read about it at wiki or read it at Gutenberg. It is a paean to the virtues of individualism and a polemic against the evils of collectivism.
Summary: our hero lives in a society where the word "I" is unknown, as are individual names; he grows up lively, interested, and questioning but is assigned the trade of street sweeper. By native brilliance and a chance discovery of ancient relics in a subway tunnel he rediscovers electricity as a source of light; when he shows this to the college of scholars they are appalled: it might put the candle makers out of business. After an obligatory torture scene - in Rand, the state must be physically violent, no matter how little it fits - he runs into the wilderness, followed by the noble upright "Golden One", a woman as unbent as him. But naturally her only desire is to obey him, and subsequently have his babies. After wanderings they find an abandoned house from The Old Times on top of a mountain; he learns to read while she admires herself in the mirror; he determines to rebuild society, starting with his infants and those from his old city not crushed.