  This review discusses progress in the new field of coherent matter waves, in
particular with respect to Bose-Einstein condensates. We give a short
introduction to Bose-Einstein condensation and the theoretical description of
the condensate wavefunction. We concentrate on the coherence properties of this
new type of matter wave as a basis for fundamental physics and applications.
The main part of this review treats various measurements and concepts in the
physics with coherent matter waves. In particular we present phase manipulation
methods, atom lasers, nonlinear atom optics, optical elements, interferometry
and physics in optical lattices. We give an overview of the state of the art in
the respective fields and discuss achievements and challenges for the future.
