Ravi Vakil gives a delightful introduction of some of the more interesting yet enigmatic areas of mathematics. Most of us are not too familiar with the cardinality of numbers or Galois Theory. However, the author presents these fascinating topics in such a lucid and insightful manner, that one becomes easily engrossed. Also, I particularly enjoyed reading the profiles of the young mathematicians - it was quite inspiring! Furthermore, the problems at the end of each section are thought provoking; many do not have complete solutions, and thus encourage the reader to think hard about them. As the title implies, it is NOT a textbook, but rather a compilation of scattered "lectures." It is a great book for the talented math reader, and students who want to explore some mathematics outside the general curriculum.