I will be talking about the length of Borel hierarchies.

My interest in this topic started with my thesis in 1979:
On the length of Borel hierarchies
Annals of Math Logic, 16(1979), 233-267.

and continues to this day:
Universal Functions
(with P.Larson, J.Steprans, W.Weiss)
eprint Apr 2012 last revised Feb 2013.

There is no textbook, however see:
Descriptive Set Theory and Forcing:
how to prove theorems about Borel sets the hard way
Lecture Notes in Logic 4(1995), Springer-Verlag.

Borel hierarchies - results, references:
bor.tex .. bor.pdf