Principles of Locally Conformally Kahler Geometry

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.