Running notes can be found here.
The primary source for the seminar is the textbook of Tao. Note the errata on his website, especially for exercises.
There is also the course in additive combinatorics by Gowers, which includes exercises, notes, and video lectures. The end of this class gets into higher order Fourier analysis. The beginning is not directly relevant for the seminar.
There are detailed lectures by Ben Green that motivate nilsequences, and a more general discussion of why nilpotent groups matter in this video.