This book is very comprehensive in the techniques and theory that it covers. I had seen some of the techniques that this book covered when reading solutions to some algebra problems that I could not solve, but I never found a resource that covered those techniques in depth except for this book. For instance, the section on factoring three variable expressions was extremely informative and helpful, as it explained the motivation and intuition behind why certain identities related to factoring worked. Another example of this is the section on fixed points and monotonicity. Its presentation is just the right balance of difficulty and depth of theory, which made it a very informative read. The examples provided in this section explained very transparently how to employ the techniques presented and helped me understand the theory beyond surface level. Moreover, the section on symmetry was also very helpful, as I had seen tidbits on using the ideas covered in the section, but they were not very detailed. Instead, this section clearly presented the theory behind symmetry, and showed specifically how to use them in examples. Also, I was trying to find a good resource on Olympiad inequalities that was somewhere in the middle terms of difficulty. Too often would I find a resource that was either too easy or too advanced. However, this book's discussion in inequalities was definitely what I was looking for, as it expanded upon the basic notions of inequalities that I knew and introduced more theory at an appropriate pace. I ended up understanding what Holder's inequality was after simply reading this book, while I got nowhere trying to understand it prior to that. The example inequalities were very beneficial for building intuition, as their solutions were well-written and motivated, and I think I got a lot out of reading and working out the details in the sections involving inequalities. Lastly, I thought that the introductory and advanced problems were excellent for learning. The problems were appropriately picked for their level, and their solutions were rather creative. The introductory problems were good for making sure that I understood the content covered in the previous sections, while the advanced problems were, as claimed, challenging. The background that was written before the presentation of the problems complemented the problem sets well. Often, I found that referring back to the background sections was helpful when trying to solve one of the problems. I believe that the advanced problems especially were perfect for cementing my understanding of the content covered, as they needed many steps, which tested the limits of my algebraic abilities. The solutions to the problems were also written very well and were clear; often, the solutions were very simple and elegant, so I was always able to get something out of them whether I had solved the problem or not. Overall, this book was very rewarding to work through, and helped me move up my algebra skillset from pre-Olympiad to Olympiad level.
