The original collection has been selected by G.Baumslag, A.Myasnikov and V.Shpilrain with the help of several other people. In particular, we are grateful to G.Bergman, G.Conner, W.Dicks, R.Gilman, I.Kapovich, V. Remeslennikov, V.Roman'kov, E.Ventura and D.Wise for useful comments and discussions. We now have over 200 open problems in our collection, and we invite the mathematical community to submit more problems as well as comments, suggestions, and/or criticism. Please send us e-mail at wwalgebra@yahoo.com