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Preliminary version

Straightening out Theorem

Preliminary version

Second order DEs and geodesics

Preliminary version

Infinitesimal Inverse Function Theorem

A derivation of Einstein’s vacuum field equations

Preliminary version

General Relativity: Affine connections, parallel transport and sprays

Preliminary version

Metrics, connections and curvature

Preliminary version

Lie derivatives, Lie brackets and vector fields over curves

Preliminary version

Curvature and Torsion of a connection

Preliminary version

The Riemann-Christoffel tensor

Preliminary version

Covariant derivation