This is a series of lectures we have held during the academic year
2004-2005 at the Department of Mathematics of the Bilkent University in
the seminar of operator theory. The theory of reproducing kernel Hilbert
spaces has important applications to boundary value problems, integral
operators, harmonic and analytic functions, in conformal mappings of
simply- and multiply-connected domains, in pseudo-conformal mappings, in
the study of invariant Riemann metrics, in probability theory,
interpolation of functions, and in many other subjects. In this short
presentation, we consider an introduction to this subject by emphasizing
first the abstract theory, the Bergman kernels, and some of their
applications to interpolation of functions in the unit disc. The book is
aimed to a broader audience of graduate students, mathematicians,
physicists, and engineers, and all those having an interest in getting a
quick, but carefully presented, mathematically sound basic knowledge on
this domain.