  This preprint mainly reflects the new chapter we are prepearing for the
second edition of our book "Gravitational Solitons" (V. Belinski and E.
Verdaguer). However, here it is written in the form of more or less
self-consistent paper dedicated to the mathematical theory of black holes
immersed in the external electromagnetic field. The purpose of this development
is to describe the procedure by which one can construct a number of axially
symmetric black holes or naked singularities arranged along the symmetry axis
and immersed in an (also axially symmetric) external electromagnetic field.
