The Light Cone coordinate was introduced as one of candidates for forms of dynamical variables by Dirac in 1949. In this coordinate, the time component of space-time four-vector at each point is perpendicular to the light cone surface. Two other different coordinate forms have been introduced by Dirac, “Instant Form” and” Point Form”. Time component in “Instant Form” is chosen as usual as we use in ordinary physics and in “Point Form” time component is perpendicular to light cone hyperboloid surface. The Light Cone Coordinate also has application in different areas of physics such as nonperturbative QCD, String theory, Ads/Cft etc. As we will show in this thesis, additional second dir=rtl align=right approach, in its ordinary framework helps us to quantize constraint system and find the commutation relations among fields and momentum fields. For this purpose we use Dirac bracket definition and finally convert it to commutator . By using this method in light cone quantization it can be depicted that the commutation relations among fields and momentum fields in this coordinate differ from ordinary ones. For instance, there is noncommutitativity between Scalar fields at equal light cone time. This noncommutitavity happens also in “Fermionic” and “Electromagnetism field”. One indirect way to find commutation relations among creation and annihilation operators in light cone quantization by Dirac method is achieved by using commutation relations among fields and momentum fields. In some models, such as “Fermionic”, “Electromagnetism” and “Yang-Mills theory” in Light Cone coordinate, we encounter a few number of constraint, hence it makes some difficulties in computing the inverse of the constraint matrix. We suggest Symplectic method to find commutation relations among creation and annihilation operators directly. As we will see, the quantization of field theory by this method is more simple than Dirac method. Symplectic approach applied in Light Cone Quantization in recent years. The Symplectic method that we use in this dissertation is based on Furrier expansion of fields and momentum fields in terms of Schrodinger modes. By applying constraint relations, the unphysical modes are removed and we can find the Dirac bracket of modes by means of Symplectic two form. By using these Dirac brackets we can also find the commutation relations among fields and momentum fields. These commutation relations are same as Dirac method. Two other problems are also discussed in this thesis, the physical modes and the propagator in Light Cone field theory. Investigating the covariance of the propagator helps us to find better the physical equivalence between different forms; in our case the Light Cone and Instant forms. In this thesis, the Dirac and Symplectic approach are used for Scalar, “Fermionic” and “Electromagnetism” field. The propagator is also computed for “Scalar” and “Fermionic” field. By applying the Symplectic approach it can be seen that extra constraints do not change the number of independent modes in three fields. The propagator of Scalar and Fermionic fields in Light Cone coordinate is computed as same as propagator in ordinary coordinate. Keywords: Light Cone Coordinate, Dirac approach, Symplectic approach