The Jones beta numbers give a measurement for how well the support of a measure may be approximated by a subspace.   We will classify those measures for which the Jones beta numbers are Dini-integrable, seeing that they are rectifiable with mass bounds.  This has applications in the structure theory of singularities of nonlinear equations, which we may touch on.  The lectures will be basic, with very little prerequisites (calculus and what is a measure...) and will focus on examples and outlining the proof structures.