I have also currently started to learn about the subject. This is some of the material I have encountered:
Many people recommend the book "The Volatility Surface: A Practitioner's Guide" by Jim Gatheral. It is a standard reference in the area (even though I personally found it a bit confusing and a bit unclear at some parts).
The author also have some lectures in the area online one can download for free.
I found a nice master thesis that explains a lot about the calibration of the local volatility surface called "Calibrating the local volatility model" by Lykke Rasmussen.
It can be downloaded online as well.
A standard reference in the area of calibrating the local vol surface is also the article "volatility interpolation" by J. Andreasen and B. Huge.
It is very brief though and do not elaborate on details, so it is a good idea to use other references at the same time.
The blog "Chase the devil" and the article "don't stay flat" by Fabien Le Floc'h contains a nice comment on the article of Andreasen, Huge about the interpolation used and suggest piecewise linear interpolation instead of piecewise constant interpolation as in the mentioned article, to avoid volatility blowups in some cases.
There is also a book called "Stochastic volatility modeling" where you can find the first two chapters for free (about local vol for among other things). You find it here:
OpenGamma also have an article called "local volatility" about interpolation of the implied volatility surface and construction of the local volatility surface.
It seems a bit too advanced for me at the moment, but it might be a good reference.