Tensor algebra -- Vector fields in affine and Riemann space -- Tensor analysis -- Tensors in physics -- The gravitational field equations in free space -- The Schwarzschild solution and its consequences: experimental tests of general relativity -- The mathematical structure of the Einstein differential system; the problem of Cauchy -- The linearized field equations -- The gravitational field equations for nonempty space -- Further consequences of the field equations -- Cosmology and astronomy -- Cosmological models -- Electromagnetism and general relativity