  We present a proof of the celebrated result due to Alexander and Hirschowitz
which determines when a general set of double points in $\mathbb P^n$ has the
expected Hilbert function. Our intended audience are Commutative Algebraists
who may be new to interpolation problems. In particular, the main aim of our
presentation is to provide a self-contained proof containing all details
(including some we could not find in the literature). Also, considering our
intended audience, we have added (a) short appendices to make this survey more
accessible and (b) a few open problems related to the Alexander-Hirschowitz
theorem and the interpolation problems.
