I would highly recomment David Duvenaud's PhD thesis [1] for anybody interested in Gaussian Processes. I find his chapter [2] on expressing structure with kernels super interesting and quite intuitive. It's also one of the PhD theses with the best-looking graphics I've read!

[1] http://www.cs.toronto.edu/~duvenaud/thesis.pdf

[2] https://raw.githubusercontent.com/duvenaud/phd-thesis/master...