  This is the introductory part of my PhD thesis on inverse problems arising in
medical and seismic imaging. The topics include X-ray tomography of scalar and
vector fields with partial data, higher order fractional Calder\'on problems,
travel time tomography on Riemannian and Finsler manifolds, and unique
continuation of fractional Laplacians. The thesis additionally includes these
articles: arXiv:1909.05585, arXiv:2001.06210, arXiv:2006.05790,
arXiv:2008.10227, arXiv:2009.01043, arXiv:2010.11484, arXiv:2103.14385.

Analysis of PDEs;Differential Geometry;Functional Analysis