An Adams Spectral Sequence Primer

My aim with these notes is to quickly get the student started with the Adams spectral sequence. To see its power requires that some concrete calculations be done. However, the algebra required can quickly become overwhelming if one starts with the generalized Adams spectral sequence. The classical Adams spectral sequence, in contrast, can be quickly set up and used to do some calculations which would be quite difficult by any other technique. Further, the classical Adams spectral sequence is still a useful calculational and theoretical tool, and is an excellent introduction to the general case. Throughout, I have tried to motivate the ideas with historical remarks, heuristic explanations, and analogy. For prerequisites, the reader should be willing to work in some category of spectra, though little more than the notion of stabilizing the homotopy types of spaces will really be needed. In particular, no familiarity with the details of any particular category of spectra will be assumed. A passing acquaintance with calculations with the Steenrod algebra will be helpful, though the details will be provided where they are needed, so a determined novice has a good chance of success.