For the moment I am done with the last part of a textbook Introduction to Stable homotopy theory
, the last part being about the Adams spectral sequence
With Firefox go tohttps://ncatlab.org/nlab/show/Introduction+to+Stable+homotopy+theory+--+2
otherwise use the pdfhttps://dl.dropboxusercontent.com/u/12630719/StableHomotopyTheory-2.pdf
The first part, in turn, of this last part, up to the discussion of convergence, provides full details with full proofs. The section on convergence presently just states Bousfield's convergence theorems, after introducing all the infrastructure needed to state and parse them. Maybe later there'll be an occasion that I add an exposition of these proofs, too.
Then the last part of the last part is a walk through the detailed computation of the classical Adams spectral sequence for the computation of the stable homotopy groups of spheres in low degrees. I spell out all the lemmas required for running the May spectral sequence for the second page and give detailed examples of the kind of computations that one needs to do, enough that the interested reader should see how to proceed.
Beware that this last part is not completely finalized towards the end, but it should be well readable already. I will get back to this later.
For the main document seehttps://ncatlab.org/nlab/show/Introduction+to+Stable+homotopy+theory