  These tutorials introduce some basics of imaging with coherent X-rays,
focusing on phase contrast. We consider the transport-of-intensity equation, as
one particular method for X-ray phase contrast imaging among many, before
passing on to the inverse problem of phase retrieval. These ideas are applied
to two-dimensional and three-dimensional propagation-based phase-contrast
imaging using coherent X-rays. We then consider the role of partial coherence,
and sketch a generic means by which partially coherent X-ray imaging scenarios
may be modelled, using the space-frequency description of partial coherence.
Besides covering fundamental concepts in both theory and practice, we also give
opinions on future trends in X-ray phase contrast imaging including X-ray
tomography, and comparison of different phase contrast imaging methods. These
tutorials will be accessible to those with a basic background in optics (e.g.
wave equation, Maxwell equations, Fresnel and Fraunhofer diffraction, and the
basics of Fourier and vector analysis) and interactions of X-rays with matter
(e.g. attenuation mechanisms and complex refractive index).
