The aim of this book is to give an introduction to theory of classical as well as general valuations. More specifially one of the persepevtive of this book is to provide an characterization of the closed subfields of a finite rank valued field. One can find generalization of some known results from classical theory of valuations. As a second aim, a Galois theory of a transcendetnal extension of valued fields is given. Which then may help to obtain new information on the structure of such subfields and implicitly, on some transcendental functions.