Week 1 — Preliminaries: review vectors, tensors, index notation, special relativity basics. Week 2 — Manifolds, coordinate transformations, metric tensor. Week 3 — Covariant derivative and parallel transport. Week 4 — Geodesics and variational derivation. Week 5 — Curvature tensors and their symmetries. Week 6 — Einstein field equations; stress–energy tensor. Week 7 — Schwarzschild metric, orbits, light deflection, tests. Week 8 — Intro to cosmology (FRW), simple problems and review.
Reading complex tensor equations on a standard e-reader can distort the formatting. High-quality PDFs preserve mathematical typesetting (LaTeX) perfectly.
Rμν−12Rgμν+Λgμν=8πGc4Tμνcap R sub mu nu end-sub minus one-half cap R g sub mu nu end-sub plus cap lambda g sub mu nu end-sub equals the fraction with numerator 8 pi cap G and denominator c to the fourth power end-fraction cap T sub mu nu end-sub the theoretical minimum general relativity pdf
However, because Susskind’s book is based directly on his Stanford University lecture series, which is publicly available.
Γμναcap gamma sub mu nu end-sub raised to the alpha power Parallel transport on curved surfaces Riemann Curvature Tensor Week 1 — Preliminaries: review vectors, tensors, index
While the allure of a free PDF is strong, respect the work. Watch the free Stanford lectures first. If you finish those and want the concise, written reference to solve the equations yourself, buy the book or the legal ebook. Your brain—and Leonard Susskind—will thank you.
Gμν+Λgμν=8πGc4Tμνcap G sub mu nu end-sub plus cap lambda g sub mu nu end-sub equals the fraction with numerator 8 pi cap G and denominator c to the fourth power end-fraction cap T sub mu nu end-sub Week 4 — Geodesics and variational derivation
Special Relativity (time dilation and Lorentz transformations).