  An LCK (locally conformally Kahler) manifold is a complex manifold admitting
a Kahler covering with monodromy acting by homotheties. Hopf manifolds and
their submanifolds are the prime examples. This book presents an introduction
to the principles of LCK geometry (the first two parts) and its current
situation (the last part). It is supposed to be accessible to master and
graduate students of complex geometry. The book contains many exercises of
different levels of difficulty. We finish it by a list of open questions.
