  The main content of this book is composed from two doctoral theses: by
V.\,V.~Katrakhov (1989) and by S.\,M.~Sitnik (2016). In our work, for the first
time in the format of a monograph, we systematically expound the theory of
transmutation operators and their applications to differential equations with
singularities in coefficients, in particular, with Bessel operators. Along with
detailed survey and bibliography on this theory, the book contains original
results of the authors. Significant part of these results is published with
detailed proofs for the first time. The book is concluded with a brief
biographic essay about Valeriy V.~Katrakhov, as well as detailed bibliography
containing 648 references.
