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Readings, organized by week, are assigned in the required textbooks:

Resnick, Robert. Introduction to Special Relativity. New York, NY: Wiley, 1968. ISBN: 0471717258.

French, Anthony Philip. Special Relativity. New York, NY: Norton, 1968. ISBN: 0393097935.

Einstein, Albert A. Relativity: The Special and the General Theory. New York, NY: Three Rivers Press/Random House, 1961. ISBN: 0517884410.

Week # Topics Readings
1 I. Introduction and Relativity Pre-Einstein

II. Einstein's Principle of Relativity and a new Concept of Spacetime
Resnick. Chapters 1 and 2, and Supplement A.

Chapter 1: "The Experimental Background of the Theory of Relativity."
Chapter 2: "Relativistic Kinematics."
Supplement A: "The Geometric Representation of Spacetime."

French. Chapters 1, 2, and 3.

Chapter 1 gives a preview of the remarkable consequences of relativity.
Chapter 2 gives a very good overview of the puzzling properties of light propagation discovered in the 19th century that led up to Einstein's formulation of relativity.
Much of chapter 3 repeats R&H. You only need to read one source.

Einstein. Chapters 1-12, and Appendix 1. (Poetry for physicists.)
2 III. The Great Kinematic Consequences of Relativity

IV. Velocity Addition and other Differential Transformations

V. Kinematics and "Paradoxes"
Resnick. Chapters 2 and 3.

French. Chapters 4 and 5, pp. 125-134.

Einstein. Chapters 12-17, and Appendix 2.
3 V. Kinematics and "Paradoxes"

VI. Relativistic Momentum and Energy I: Basics
Resnick. Chapter 3, Supplements A and B. (Supplement A was also assigned on problem set 1, now would be a good time to study it further.)

French. Chapter 5, pp. 134-159, chapter 6.
4 VII. Relativistic Momentum and Energy II: Four Vectors and Transformation Properties

VIII. General Relativity: Einstein's Theory of Gravity
Resnick. Chapter 3 and Supplement C (on General Relativity).

French. Chapter 7 (and chapter 6, if you have not studied it yet).

Einstein. Chapters 18-29. (General Relativity in Einstein's own words.)