I would first like to mention that I am a fan or both Horowitz and Reinfeld. While their books are not very dense, they are extremely readable and focus on the most important concepts without getting lost in a lot of unnecessary detail. I believe that to some extent, what books work best for different people depends upon how they learn. For how I learn, this is a great approach and in addition to learning new things I enjoy the process of learning. This makes it more likely that I will actually finish the book!
As many other reviewers mention, this book is not for the absolute beginner. For example, it doesn't teach how the pieces move and basic rules. It is for a beginner who wants to take their game to the next level by understanding elementary openings, the principles behind various tactis and get a sense for strategic planning.
The authors achieve their pedagogical goal by looking at illustrative games between amateurs for the most part. They discuss alternative lines of play, but not in such detail that it is distracting. You can probably follow most of the chapters without pulling a board out, but I recommend putting the example games in a computer and reviewing the various lines until you digest all the principles completely.
As the book proceeds, it develops various themes in an overall context. I think this helps a lot with recall and integrating the knowledge so that it is useful. For example, the first game introduces the Ruy Lopez opening, pinning, tactical use of pawns, how oversights tend to occur, etc. The next chapter builds on this and looks at a different opening and some traps that can occur. All the examples are carefully chosen and by the time you finish the book you will understand a lot more about position, tactics, planning, etc. In short, you will improve your game significantly!
A lot of chess books teach various aspects of the game, but sometimes they fall short with respect to getting the information across in a way that is practical for direct application. This has NOT been the case for me and I have found this book and others by these authors good. They have withstood the test of time and I have no problems with the old chess notation at all. It is quite logical and straightforward. If you are not familiar with it you will catch on quickly. This book provides integrated learning. In this sense, I think it is a simple, but ingenious approach because it gets you thinking like a better chess player without you hardling noticing the learning process.
If you are a beginner, you may want to read HOW TO BE A WINNER AT CHESS by Reinfeld first. This book contains more basics and a good foundation in the game as a whole. The book I'm reviewing is a perfect follow up. If you are looking for something more modern, but that also requires more dedication then HOW TO REASSES YOUR CHESS is wonderful and well thought out. You can also get the HOW TO REASSESS YOUR CHESS WORKBOOK, which is a useful tool to accompany this book.
Ideally, if you are serious about getting better, but are intimidated by most chess books, I think you will benefit from HOW TO IMPROVE YOUR CHESS. It will also prepare you for the more rigorous HOT TO REASSESS YOUR CHESS, which is a nice intermediate step to some more advanced books. You can get Horowitz's and Reinfeld's books very inexpensively used. You might want to try one of these and see how their style appeals to you. If you are intimidated by the average chess book, you might also like Chris Ward's style of teaching and writing. He has books on the VERY basics of the openings and logic behind them, endgame strategy, etc.
The more straightforward books like Chris Ward's are also useful for younger people who haven't quite developed a passion yet, but still have some desire to know more and improve their games incrementally. I know there are other more popular and perhaps better written books out their for various audiences, but for some specific readers I think these might be an even better fit. I was a Director of Education for a major company and taught at both the university and high school levels. Based on my experience, different people have different learning styles and each person needs to find what works best for THEM. Often a mixture of styles is the best approach and actually what I use to digest large amounts of information quickly.