Left amenability of semigroups was introduced by day, in the 1940s. amenability of groups and semigroups is motiration for extreme Left amenability introduced by Granirer in the 1960s. extreme amenabilityturn out to be equivalent to a very strong nonlinear fixed point property, but examples topological groups having this property are rather hard to consttruct. the purpose of this thesis is to expand an study of an intermediate property, called strong Left amenability, introduced by Bouffard in 2011.