Nine Algorithms That Changed the Future (2013) by John MacCormick is a well written good read that looks at exactly what the title suggests. The book covers indexing, pagerank, public key cryptography, error correcting codes, pattern recognition, data compression, database algorithms, digital signatures and also covers computability.
The chapters do involve thought and the book isn’t a completely light read. But it’s well worth it. Along with Patterns in The Stone this is one of the best books I’ve seen that explains computing concepts clearly to people who are not programmers.