  This PhD dissertation is concerned with integral geometric inverse problems.
The geodesic ray transform is an operator that encodes the line integrals of a
function along geodesics. The dissertation establishes many conditions when
such information determines a function uniquely and stably. A new numerical
model for computed tomography imaging is created as a part of the dissertation.
The introductory part of the dissertation contains an introduction to inverse
problems and mathematical models associated to computed tomography. The main
focus is in definitions of integral geometry problems, survey of the related
literature, and introducing the main results of the dissertation. A list of
important open problems in integral geometry is given.
  The four articles of the dissertation (arXiv:1705.10126, arXiv:1901.03525,
arXiv:1906.05046, arXiv:1909.00495) are now published in various journals and
the content of the document has not been updated since November 11, 2019. These
four articles are omitted from this document which contains only the
introductory part. Extended abstracts are given in the document in English and
Finnish.
