  As has been known since the time of Gromov's Nonsqueezing Theorem, symplectic
embedding questions lie at the heart of symplectic geometry. After surveying
some of the most important ways of measuring the size of a symplectic set,
these notes discuss some recent developments concerning the question of when a
4-dimensional ellipsoid can be symplectically embedded in a ball. This problem
turns out to have unexpected relations to the properties of continued fractions
and of exceptional curves in blow ups of the complex projective plane. It is
also related to questions of lattice packing of planar triangles.
