This text will be potential great interest to three different groups of readers. The first group of readers will be interested in the history and biographies of the mathematicians and physicists who developed and used differential geometry and forms. As stated  the text can be read at this level with a basic understanding of calculus and geometry. The many places in the text left as excercises and the problems can be skipped. Get an idea off what differential geometry and forms are about. The excellent drawings and numerous drawings make the book a pleasure to read. Clearly 5 stars.<br> If you are a self learner interested in learning differential geometry and forms, the book is more problematic. The subject of tensors and differential forms is well covered in the fifth section. If you are familiar with contravariant, covector, and duality from previous study of tensors, this section of the book will help you understand df, dx,dy, and dz as one forms. There is nice introduction to external derivatives, wedge products, Maxwell's equations, spacetime and curve space.  Peter Collier's recent publication on this subject is a much easier read but the math by Needham is much more rigorous. As the author suggests section 5  (act 5) of the book can be read separately. You might want to read Fleisch's Maxwell's Equations and Vectors texts before reading Act 5. You also should consider Guidry's  Modern General Realtivity. The review of tensors and Jacobians in Chapter 3 of Guidry's text is superb.<br>There are some issues for self learners in the first four acts of Needham's text. There should be a online site to see the suggested excercises in the text. The chapters with multiple unsolved problems are frustrating. They are perfect for advanced undergraduate math or physics majors. This would allow  the text to be used in a classroom setting with teaching assistants. That being said the differential geometry explored in these chapters is beautiful. It is rewarding to try to understand the geometry and compare it with the results from vector calculus.<br>I will leave it to the physics and math experts to review the text as a classroom standard or supplemental text. The text clearly is 5 stars at many levels. A second version written for self learners would be wonderful. If you are a self learner, you may give the book a lower score. A book with solved problems  for self learners would be beautiful.  The author Tristan Needham  deserves our thanks for his beautiful text.