This book is an introduction to the subject of mean curvature flow
of hypersurfaces with special emphasis on the analysis of
singularities. This flow occurs in the description of the evolution
of numerous physical models where the energy is given by the area
of the interfaces. These notes provide a detailed discussion of the
classical parametric approach (mainly developed by R. Hamilton and
G. Huisken). They are well suited for a course at PhD/PostDoc level
and can be useful for any researcher interested in a solid
introduction to the technical issues of the field. All the proofs
are carefully written, often simplified, and contain several
comments. Moreover, the author revisited and organized a large
amount of material scattered around in literature in the last 25
years.
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