Originally called simply "Chess" when printed in Russian, this book was widely used as an early instruction handbook for Soviet chess players. Far be it from me to want anything to do with the Soviet Union, but even I have to admit, this is one of the finest tools to quickly advance your chess game if you're an advanced beginner or intermediate player.
Where I think some people may become a bit confused is the word "primer" in the title. Though this book does begin with the basic rules of chess--and even teaches the reader how to read the book because it takes the time to explain algebraic chess notation right at the start--it quickly moves on to more advanced tactical and strategic ideas. Beginners who genuinely are just learning the basic rules of the game could hypothetically read this book, but I think they will very quickly become overwhelmed by the more advanced ideas discussed even as early as the second or third chapters.
However, readers who already have some familiarity with the game will benefit a lot from its discussions of ideas which are fairly simple to understand but often difficult to apply in real games. For example, simple tactics like pins and forks are easy enough for even absolute beginners to understand. However, where this book shines is that it provides enough examples (of increasing complexity) that reading the book will help the reader begin to recognize when those tactics might become relevant. Chess is largely a matter of pattern recognition, and this book will help you start to recognize the patterns.
Ultimately, I'd recommend this for the serious beginner or early-intermediate chess player looking to deepen his or her knowledge of the game.