**Thesis Type:** Postgraduate

**Institution Of The Thesis:** Bursa Uludağ University, Fen Bilimleri Enstitüsü, Turkey

**Approval Date:** 2016

**Thesis Language:** Turkish

**Student:** Zafer Altın

**Supervisor: **ZERRİN KIRCA

In this thesis, The Littlest Higgs Model (LHM) is studied. This model is constructed to solve the hierarchy problem in the Standard Model (SM). Higgs is considered as a Pseudo-Goldstone boson in this model. LHM is based on a global SU(5) symmetry breaking down to a global SO(5) symmetry via non-linear sigma model. As a consequence of this breaking heavy gauge bosons (W(H), Z(H), A(H)), a complex doublet (h(+),h(0)) and a complex triplet (phi(0),phi(+),phi(++)) emerge in this model. Beside the heavy particles, there are light gauge bosons (W(L), Z(L),A(L)) which correspond the SM gauge bosons. In addition these particles, a vector-like quark field (T) is defined in order to cancel higher order divergent quantum corrections to the Higgs boson mass from the SM top quark (t). After the symmetry breaking all these defined particles mix with each other as well as with the SM particles. LHM has four free parameters; f, s, s', and x(L). f is the symmetry breaking scale of the model, s and s' are weak mixing angles of SU(2) and U(1) respectively, and x(L) is the parameter which determines the mixing between the SM top quark (t) and the heavy top quark (T) proposed by the model. In LHM associated production of the heavy W boson, heavy top quark (T) and bottom quark in the linear electron-positron colliders are investigated in terms of the free parameters of the model.