Lethulwe, Neo2016-09-162016-09-162016-09-16http://hdl.handle.net/10539/21043A research project submitted in partial fulfilment of the requirements for the degree of Master of Science School of Mathematics, University Of Witwatersrand 18 May 2016A topological group is called resolvable (ω-resolvable) if it can be partitioned into two (into ω) dense subsets and absolutely resolvable (absolutely ω-resolvable) if it can be partitioned into two (into ω) subsets dense in every nondiscrete group topology. These notions have been intensively studied over the past 20 years. In this dissertation some major results in the field are presented. In particular, it is shown that (a) every countable nondiscrete topological group containing no open Boolean subgroup is ω-resolvable, and (b) every infinite Abelian group containing no infinite Boolean subgroup is absolutely ω-resolvable.enTopological groups.Thesis