I have owned this book for a month or so now and have been using it primarily for the algebra chapters. So far, it has exceeded my expectations.<br><br>Depth. This book is pretty thick (3", actually). There are 37 chapters grouped into 10 parts: Finite Vector Spaces, Infinite Vector Spaces, Complex Analysis, Differential Equations, Operators, Green's Functions, Groups/Representations, Lie Groups, and Fiber Bundles. Hassani actually renders quite a few of my other books unnecessary.<br><br>Clarity. Concepts are explained clearly and the author really tries to help you understand the abstract concepts that are presented within. Take, for instance, the section on group actions. Following five definitions thrown at you in a single paragraph, you are presented with Remark 23.3.1:<br>"... If you think of G_m [the stabilizer of m] as those elements of G that are confined to (stuck, or imprisoned at) m, then a "free" action of G does not allow any point of M to imprison any subset of G. ..."<br><br>Referencability. Typically textbooks have to make tradeoffs between being good learning material and being a good reference. Hassani I would say does both well. While being very clear and readable, the book is also arranged very nicely for anyone looking for a reference textbook. Important definitions and theorems are boxed and key points are summarized in the margins.<br><br>In addition, each section contains historical notes about various mathematicians and physicists that are quite interesting to read. I do still have a couple of small complaints, though. The first is the size of the book. The thickness of the pages renders the book very large which makes it difficult to transport and to read on the bus. Given the range of topics covered, I would prefer the book be split into multiple volumes. Secondly, though I did mention clarity as a strength of this book, this does vary somewhat from chapter to chapter and some topics (the geometry chapters in particular, Clifford algebras especially) seem to be following a define-first-motivate-later approach.