Quantum dots are a kind of produced artificial atoms and typically, these are small regions of a semiconductor material with a size of order 100 nm. A quantum dot is a nano crystal conducting device including of to several thousand electrons. Traort through a quantum dot is an example of quantum coherent process at low temperatures. Quantum dots are usually made by forming a two-dimensional electron gas in the interface region of a semiconductor heterostructure GaAs-AlGaAs and adding an electrostatic potential to metal gates to further confine the electrons to a small region “dot” in the interface plane. A quantum dot is sometimes referred to as a zero-dimensional system and its the result of restriction electronic motion in all three dimensions and quantum confinement. One of the main features of a quantum dot can be explained by coupling it to leads and passing current along the dot. Quantum dots put into a larger left; MARGIN: 0cm 0cm 0pt; unicode-bidi: embed; DIRECTION: ltr; tab-stops: 45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt" align=left Coupling the electron to its environment can affect phase coherence and phase-breaking processes make a change in the state of the environment. Microscopic theory of quantum traort including interactions can be explained by Non-equilibrium Green's function (NEGF) formalism which combines quantum dynamics with a statistical description of the dissipative interactions.The real power of this formalism is presenting a general approach to dscribe quantum traort in the presence of interaction. In this thesis we consider a double quantum dot structure in a parallel geometry which is connected to two linear chain metal leads.The transient electric current through this construction is studied by non-equilibrium Green’s function formalism in zero temperature.