This is a book review of Our Mathematical Universe: My Quest for the Ultimate Nature of Reality by Max Tegmark. Tegmark's book is a popular exposition of astronomy (Part One) as well as quantum mechanics (Part Two), leading up to his mathematical-universe hypothesis (Part Three). Tegmark is careful to distinguish between what is mainstream and what is (very) controversial as well as between his own work and the work of others. While the emphasis of the book is on a controversial idea of Tegmark, it is important to note that most of his work, some of which is also discussed in the book, is mainstream (and also that he discusses some controversial ideas due to other people). The multiverse has been mentioned by many others, but Tegmark gives a good overview of the various concepts involved. The point is stressed that multiverses are not a theory, but rather testable consequences of other theories. Even if some multiverse might not be directly detectable itself, it might be justified by confidence in the theory on which it is based, much as we believe what General Relativity tells us about the interior of black holes, even though these are almost as inaccessible to us as are other parts of a multiverse. Although this is by no means proof, at least some multiverses are an extension of a trend which has been going on for quite some time: Earth is just one of many planets, our galaxy just one of many galaxies etc. Readers should keep an open mind and follow the arguments closely. I highly recommend the book. Not all readers will agree with Tegmark on all points, but any disagreement will take place on a level high enough that the journey there will have been worth it for its own sake.