  The planar front of a growing a crystal is often destroyed by instabilities.
In the case of growth from a condensed phase, the most frequent ones are
diffusion instabilities, which will be but briefly discussed in simple terms in
chapter II. The present review is mainly devoted to instabilities which arise
in ballistic growth, especially Molecular Beam Epitaxy (MBE). The reasons of
the instabilities can be geometric (shadowing effect), but they are mostly
kinetic or thermodynamic. The kinetic instabilities which will be studied in
detail in chapters IV and V result from the fact that adatoms diffusing on a
surface do not easily cross steps (Ehrlich-Schwoebel or ES effect). When the
growth front is a high symmetry surface, the ES effect produces mounds which
often coarsen in time according to power laws. When the growth front is a
stepped surface, the ES effect initially produces a meandering of the steps,
which eventually may also give rise to mounds. Kinetic instabilities can
usually be avoided by raising the temperature, but this favours thermodynamic
instabilities. Concerning these ones, the attention will be focussed on the
instabilities resulting from slightly different lattice constants of the
substrate and the adsorbate. They can take the following forms. i) Formation of
misfit dislocations (chapter VIII). ii) Formation of isolated epitaxial
clusters which, at least in their earliest form, are `coherent' with the
substrate, i.e. dislocation-free (chapter X). iii) Wavy deformation of the
surface, which is presumably the incipient stage of (ii) (chapter IX). The
theories and the experiments are critically reviewed and their comparison is
qualitatively satisfactory although some important questions have not yet
received a complete answer.
