While this will not make you a mathematical wizard, it does try and explain calculus, complex numbers (and quaternoins) as well as a host of mathematical topics in laymen terms. Penrose does not stop there – he moves on to advanced topics such as Riemann Surfaces, Group theory (lie groups),  fiber bundles, twistor theory (to which Penrose contributed heavily ) and other advanced topics. He offers the reader the option of skipping the math and reading the physics applications of the math. For those interested in problem solving, interesting problems accompany most chapters. His treatment of complex number calculus and his chapter on Quantum Entanglement stand out as above par. If you ever struggled to understand the value of complex numbers or how they simplify actual problem solving, Penrose provides simple and elegant explanations. There is no doubt that a book of such grandiose breadth will attract critics, but overall, the book has more ‘goodies’ than negatives.  It is targeted towards a very large audience – from high school students (with some physics and calculus) to the advanced undergraduate student to the layperson with some mathematical exposure – looking to learn more.<br><br>While not an easy read, it is a great starting point for anyone looking to get back into physics  - by approaching it from the mathematical side (Penrose is actually a mathematical physicist  - he holds one of the most prestigious chairs in the world of mathematics). For those who are interested in the NEXT book after this one, I had compiled a list of similar 'self learning' books :<br><br>http://www.anujvarma.com/self-learning-booksfor-advanced-physics/