Can you recommend problem and solution books on algebraic topology?”
There’s a free book you can download here: http://www.math.cornell.edu/~hatcher/AT/ATpage.html And you should consider this one. It’s not a workbook exactly, but it does have problems and solutions as well as theory which may be of interest to you: A Concise Course in Algebraic Topology (Chicago Lectures in Mathematics) (Paperback) by J. P. May List Price: $22.00 Price: $18.92 & eligible for FREE Super Saver Shipping on orders over $25.