I first learned GPs about two years back, and have been fascinated by the idea. I learned it through a video by David MacKay, and managed to grok it enough that I could put it to use in simple settings. That was reflected in my Flu Forecaster project, in which my GPs were trained only on individual latent spaces.
Recently, though, I decided to seriously sit down and try to grok the math behind GPs (and other machine learning models). To do so, I worked through Nando de Freitas' YouTube videos on GPs. (Super thankful that he has opted to put these videos up online!)
Secondly, I have also put together some hand-written notes on GPs. (For those who are curious, I first hand-wrote them on paper, then copied them into my iPad mini using a Wacom stylus. We don't have the budget at the moment for an iPad Pro!) They can be downloaded here.
Some lessons learned: