Spectral sequences on their own right

Question

I have begun to read a bit about Spectral Sequences. I have been studying some topics of algebraic topology and this "tool" came up from time to time. I didn't need to go deep, but I felt I had to read a bit. Things started to get more delicate, e.g. the Adams S.S., and more stuff. So I wondered (before attempting this), if these things are important in their own right. I guess so, but I wonder what part of mathematics concentrate on them, and what "gadgets" and conjectures exist about them, independently if may be of where you will use them. I would ask for reference, also, thanks in advance.

Answer 1

Spectral sequences are very useful, but they’re not studied in their own right. The book of McCleary, “User’s Guide to Spectral Sequences”, is the most extensive reference.

Answer 2

Actually, spectral sequences are studied in their own right as a technical tool. The first spectral sequences you see are probably the bounded ones, like first-quadrant spectral sequences. Those are pretty easy to use. But there are some subtle convergence questions that arose when more advanced spectral sequences were necessary.

A classic is Boardman's "Conditionally Convergent Spectral Sequences", where he develops convergent criteria for half-plane and whole-plane spectral sequences. The main focus of this paper is the study of spectral sequences.