  Boundary conformal field theory is the suitable framework for a microscopic
treatment of D-branes in arbitrary CFT backgrounds. In this work, we develop
boundary deformation theory in order to study the changes of boundary
conditions generated by marginal boundary fields. The deformation parameters
may be regarded as continuous moduli of D-branes. We identify a large class of
boundary fields which are shown to be truly marginal, and we derive closed
formulas describing the associated deformations to all orders in perturbation
theory. This allows us to study the global topology properties of the moduli
space rather than local aspects only. As an example, we analyse in detail the
moduli space of c=1 theories, which displays various stringy phenomena.
