Ciupeanu, Adriana-Stefania2019-12-122019-12-122019-12-022019-12-02http://hdl.handle.net/1993/34404This thesis provides a review of left-ordered groups and amenable groups. These are used to investigate a conjecture by Peter Linnell, which relates the existence of a nonabelian free group to a strengthening of left-orderability, by examining three research articles. Lastly, we propose a possible generalisation of a theorem by Dave Witte Morris and Peter Linnell.engmathematicsLeft-Orderable Groupsmaster thesis