| Some comments and links: | I taught a 9-hour version of this course at a Summer School on Stochastic PDEs at MSRI in 2014. Despite the SPDE title, most material covered in that course was more basic. Video recordings of those lectures are available on the MSRI page.
It also contains a link to my slightly older lecture notes. My plan for this semester is to improve those notes thoroughly, rewriting, amending, and correcting them as we go. That is why instead of giving a direct link to the old version here, I will post improved portions of the new notes as they become available. Besides that, there will be no official textbook. Some reading recommendations will be given in class. Several lecture sets on ergodicity for Markov processes and some SPDEs by Martin Hairer are available online: 1,
2,
3.
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