Introduction: the problem of determining a metric by its hodograph and a linearization of the problem; the kinetic equation in a Riemannian manifold. Part 1 The ray transform of symmetric tensor fields on Euclidean space: the ray transform and its relationship to the Fourier transform; description of the kernel of the ray transform in the smooth case; equivalence of the first two statements of theorem 2.2.1 in the case n=2; proof of theorem 2.2.2.; the ray transform of a field-distribution; decomposition of a tensor field into potential and solenoidal parts; a theorem on the tangent component; a theorem on conjugate tensor fields on the sphere; primality of the ideal ([x]2, ); description of the image of the ray transform; integral moments of the function I f; inversion formulas for the ray transform; proof of theorem 2.12.1; inversion of the ray transform on the space of field-distributions; the Plancherel formula for the ray transform; applications of the ray transform to an inverse problem of photoelasticity; further results. Part 2 Some questions of tensor analysis. Part 3 The ray transform on a Riemannian manifold. Part 4 The transverse ray transform. Part 5 The truncated transverse ray transform. Part 6 The mixed ray transform. Part 7 The exponential ray transform (Part contents)
