The famous mathematician William Thurston, in an article, wrote about the meaning of giving a proof for a theorem. The point was the following. "What is the meaning of giving a proof for a theorem? When I was a college student, I couldn't understand that we have to prove something even though we can fully understand it. Even now, I have such an attitude. What we want is not giving a formal proof, but understanding". After reading the article, I was deeply moved and my attitude also has changed. What we want is understanding! A lecture or a book is valuable only if it helps us understand. In this sense, R. Shankar's Fundamentals of Physics is a fascinating introduction to physics.<br><br>The focus of this book is not to list basic facts of physics and give its explanations, but to help us understand what physics is from the scratch. Even though its style is rather philosophical and fundamental, it is informal, lucid, practical, concrete (several examples for each subject).<br><br>If you have a firm understanding of calculus and calculus of several variables, then it will be very helpful for you to read the book. By firm understanding of calculus, I mean the full understanding of basic concepts in calculus, for example, the meaning of derivative and differentials in finding approximate solutions, not various techniques of integrations. If you are a mathematician, then you will find that the author understands calculus deeply and accurately. I have studied calculus of several variables, but the content of the final chapter on statistical mechanics using it was difficult for me. I think it was not because of mathematics, but because of physics.<br><br>There are several classical introductory books on physics. Among them, I'd like to compare the book with the Feynman Lectures on Physics. I just read a few chapters of Feynman's book. But I felt that he was saying too many things, and so for many freshmen, it might be confusing and difficult. But Shankar's book is more concise and easy. He seems to try to guide as many students as possible. You can find his online lecture of the book. If you watch his online lecture, you will see that he always wanted to be assured if the students understood the lectures. For example, he loves to hear questions. In fact, the book is a fruit of the online lectures at Yale University. His online lectures are easier than the book in many parts. The online lecture and the book are complementary. I first saw the online lecture corresponding to each chapter, and next, I studied the chapter of the book. This learning style was very good to me.<br><br>The followings are detailed appreciation.<br><br>1. There are three chapters on rotational mechanics in the whole 24 chapters. Before I go through, I thought it might be boring. What I desperately wanted to know were the first principles, not its applications, as far as I know, rotational mechanics belong to the latter. But my anticipation was wrong. They were really fascinating lectures. In fact, 23 years ago, as a freshman in physics department, I studied physics 101. At that time, this part was just some listing of facts to be memorized. But the book was different in that it explains rotational mechanics very kindly, step by step, from the three laws of Newtonian mechanics and the definitions of torque and angular momentum. In the chapters, there are also good examples that make readers feel as much that they understood everything the author said. In a paragraph, the author says, "the center of mass is not a physical entity". This kind of sentences makes reader to think that physics is a really concrete subject so that, in principle, we can understand physics in every detail. In almost every section, there are such sentences.<br><br>2. Do you know what a gyroscope is? It is a really amazing thing. How is it possible that the top does not fall? How can you explain it with ordinary language? Before I read the book, I didn't know what the physical principles of the gyroscope are. After reading, I still don't understand why the top does not fall. This is not because the book failed to give an explanation. I searched several books and websites. What I come to know is that the mechanism of the gyroscope can be explained by classical mechanics, but there is no intuitive explanation of it: mathematics can explain it, but physics of the level of everyday experience cannot. I was shocked from this realization. The mysteries are not only quantum mechanics, relativity, and chaos. There is another mystery near at hand: a gyroscope that is a something we can play with whenever we want (you can buy it in less than 10 dollars).<br><br>3. In the chapters on waves, he explains the velocity of sound as a wave moving through a medium, air. The velocities according to different observers can be different. His explanation for that was very clear.<br><br>4. But not all is well about this book. At some places, you would not understand what the author says until you see the online lecture, and vice versa. Reading the chapter on mathematical methods, I thought I would be able to explain more clearly than the author. The sections on the derivation of the wave equation, gyroscope, and statistical mechanics were hard to understand.<br><br>5. Among this entire good lecture, what is the best lecture? I cannot choose one. I'd like to mention two parts, the chapters on fluid mechanics and on relativity. If you think fluid mechanics is uninteresting and relativity is confusing, then I recommend the book to you. You will find that fluid mechanics is really easy and interesting, and relativity is understandable even to lay people if you don't try to understand everything the author says but you believe there are perfect explanation for that somewhere in a book (maybe in library at heaven?) and just try to understand points.