This product, a 1200- page encyclopedia of graduate-level mathematical physics, is a sequel to the author's "Mathematical Methods for Students of Physics," a book not only written with undergraduates in mind instead, but one that also carries subjects like Complex Analysis, Differential Equations and Tensors nearly seamlessly with this volume, making these two works a two-thousand page masterpiece deserving of its place by Gravitation and Classical Physics on my shelf.<br><br>Starting with finite-dimensional vector spaces (ending all the way over in the Polar Decomposition, meaning this is very nearly a self-enclosed course in applied Linear Algebra including operator theory!), the book then addresses infinite-dimensional vector spaces like Hilbert Spaces, orthogonal polynomials and everyone's favorite Fourier approximation methods. The third subect continues the earlier volume's Complex Analysis work, ending in advanced topics like the all-important meromorphic functions, but reviewing a bit more from the earlier volume with other topics like the Cauchy integral (while adding critical methods like the Principal Value, as well).<br><br>After continuing the Differential Equations sections from the earlier volume, capping off with a treatment of Sturm-Liouville, the volume continues with group and Lie theory before moving on to the section I've gone in depth on the most - tensors and differential geometry. This is a well-done section respectful of the mathematics behind the treatment. Gauges and Calculus of Variations are also included here. Although Hassani is an admitted "diffy-phile," I think this part - from Group/Lie to Riemannian/Gauge - is the best part of this amazing tome. This will give me years of learning and re-learning.<br><br>If you are a mathematical physicist or are interested in it as a possible area of exploration as a critical link between these two regal disciplines, buy this book, and buy its prequel, Mathematcal Methods for Students of Physics. These combine to form two thousand pages of a classic in the making for this field.<br><br>The only critique - apart from occasional grammar and other typos bespotting Springer publications lately - is a heavier preference for mathematcial notation over the home team notation for physics. I suppose I could also throw in a weakness with Probability and Statistics - which is only really covered briefly at the end of the preceding volume. These are nothing to the value the book gives, however. Get both in this set!