The first formulations of linear boundary value problems for analytic
functions were due to Riemann (1857). In particular, such problems
exhibit as boundary conditions relations among values of the unknown
analytic functions which have to be evaluated at different points of the
boundary. Singular integral equations with a shift are connected with
such boundary value problems in a natural way. Subsequent to Riemann's
work, D. Hilbert (1905), C. Haseman (1907) and T. Carleman (1932) also
considered problems of this type. About 50 years ago, Soviet
mathematicians began a systematic study of these topics. The first works
were carried out in Tbilisi by D. Kveselava (1946-1948). Afterwards,
this theory developed further in Tbilisi as well as in other Soviet
scientific centers (Rostov on Don, Ka- zan, Minsk, Odessa, Kishinev,
Dushanbe, Novosibirsk, Baku and others). Beginning in the 1960s, some
works on this subject appeared systematically in other countries, e. g.,
China, Poland, Germany, Vietnam and Korea. In the last decade the
geography of investigations on singular integral operators with shift
expanded significantly to include such countries as the USA, Portugal
and Mexico. It is no longer easy to enumerate the names of the all
mathematicians who made contributions to this theory. Beginning in 1957,
the author also took part in these developments. Up to the present, more
than 600 publications on these topics have appeared.