  This monograph is dedicated to a generalization of the L\"owner equation in
its stochastic form known as SLE and to its coupling with the Gaussian free
field, ultimately aiming at the construction of a boundary conformal field
theory with one free scalar bosonic field. This study is presented in line with
a systematic, and hopefully concise, presentation and generalization of known
elements of the theory of L\"owner evolution. We also study the relation to
singular representations of the Virasoro algebra and methods of numerical
simulation. The main results are in the proof of the basic properties of the
generalized SLE and general necessary and sufficient conditions for the
coupling. We also introduce a machinery that possesses to consider all L\"owner
equations and known types of the coupling as different manifestations of the
same thing.
