In my talk I am going to remind you what is the AK-invariant and give examples of its usefulness. I shall also discuss basic conjectures about this invariant and some positive and negative results related to these conjectures.
Department of Mathematics & Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel, E-mail: lml@macs.biu.ac.il, Department of Mathematics, Wayne State University, Detroit, MI 48202, U.S.A., E-mail: lml@math.wayne.edu