Formulation of field theories in light-cone coordinates are different from ordinary coordinates, which causes the light-cone coordinates to have some applications in high energy physics, especially in string theory and QCD . One of the differences is changing the constraint structure of field theories in light-cone coordinates. This makes some difficulties in quantization procedure. For example, we show that the Klein-Gordon theory, which is not a constrained system in the ordinary coordinates, becomes a constrained theory in the light cone coordinates; hence, we should use the Dirac quantization approach or some alternative one to quantize this theory. In this thesis, at first, we have investigated how non-diagonal form of light-cone metric cause changes in constraint structure of different theories. Then we have shown that these changes in constraint structure reduced the number of degrees of freedom as well as the number of independent physical modes. We investigate the effect of this fact on the procedure of solving the equations of motion and finding the Schr?dinger modes. In fact, we show that by going to the light-cone coordinates, the number of Schr?dinger modes is divided by two due to the additional constraints, but it “should” not mean that there is a difference in physical consequences and interpretations. The reason is that, as we show, the non-diagonal form of the metric enables us to divide the phase space into two parts which each Schr?dinger mode play different role in each part, so we will have same physical interpretation in analogy with the ordinary coordinates. As applications, we have quantized th e complex and real Klein-Gordon fields using the symplectic approach. Then, we have investigated the consistency of these theories in light-cone and ordinary coordinates. We have also quantized the electromagnetic theory in light-cone coordinates by choosing the appropriate gauge fixing conditions. We have then formulated Non-Abelian Yang-Mills theory in light-cone coordinates and apply appropriate gauge fixing conditions to this theory. We show that, in this case we cannot use a simple Fourier expansion of fields and conjugate momentums to quantize this theory. Keywords: symplectic quantization, constraint structure, light-cone coordinates.