  We present some old and recent regularity results concerning minimal and
almost minimal sets in domains of the Euclidean space. We concentrate on a
sliding variant of Almgren's notion of minimality, which is well suited in the
context of Plateau problems relative to soap films. We are especially
interested in regularity properties near a boundary curve, where we would like
to get a local C1 description of 2-dimensional almost minimal sets in the
spirit of J. Taylor's theorem, but we first study weaker and more general
results (local Ahlfors regularity, rectifiability, limits, monotonicity of
density), which we describe far from the boundary for simplicity. There we
insist on some simpler techniques, in particular the use of Federer-Fleming
projections.
