Inverse scattering problems for time harmonic waves are of fundamental importance in applications such as radar and sonar, nondestructive evaluation, geophysical exploration, medical imaging and others. In principle, in these applications the wave scattered by an unknown object is measured at a number of discrete locations and information such as shape parameters, location parameters and electromagnetic parameters of the scatterer are extracted from these data. In this study, a new second order Newton method for reconstructing the shape of a arbitrary cylindrical perfectly electrical conducting (PEC) scatterer from the measured far-field pattern for scattering of time harmonic plane waves is presented the first time in this thesis. This method extends a hybrid between regularized Newton iterations and decomposition methods. The main idea of our iterative method is to use Huygen's principle, i.e., represent the scattered field as a single-layer potential. Given an approximation for the boundary of the scatterer, this leads to an ill-posed integral equation of the first kind that is solved via Tikhonov regularization. Then, in a second order Taylor expansion, the PEC boundary condition is employed to update the boundary approximation. In an iterative procedure, these two steps are alternated until some stopping criterium is satisfied. Main advantages of method is that method does not need forward solver in each iteration step and needs less iteration than first order Newton method in order to obtain desired accuracy. Although there are a few results available on the convergence of regularized Newton iterations for in-verse obstacle scattering problems, this issue is not satisfactorily resolved. Despite the progress made with this espect, so far it has not been clarified whether the general results on the solution of ill-posed nonlinear equations in a Hilbert space setting are applicable to inverse obstacle scattering or, in general, to inverse boundary value problems in the frame work of solving the operator equation. This remark also implies to the convergence results of researches on the second order method with respect to its applicability for the inverse obstacle scattering problem. The more problem oriented approaches for a convergence analysis suffers from the restrictive assumption of a non vanishing normal derivative of the total field on the boundary in the case of exact data. Furthermore, in the analysis for noisy data, convergence for the noise level tending to zero, as usual, requires a stopping rule and with this particular rule the method has not yet been numerically implemented. D? These comments also apply to the case of the first order method of Kress and Serranho. At present only convergence results in the spirit of Potthast are available in literature. Therefore, we view it as legitimate to present our second order variant of this approach without a detailed convergence analysis and confine ourselves to some heuristic considerations. Of course, as in all of the iterative methods for the inverse obstacle scattering problem, the ill-posedness corrupts the high order convergence. Here, the ill-posedness enters through the integral equation of the first kind leading to inevitable errors occurring in its regularized solution. It is to be expected that a convergence analysis with respect to the noise level can be carried out analogous to the first order method. We refrain from working out the details since the result would be of a qualitative character only and would not lead to the possibility for a quantitative comparison on the convergence for the first and second order method. However, from the better convergence order for the exact data case one might expect some advantages in the numerical performance. Indeed, our numerical examples in the next section illustrate an improvement in the quality of the reconstructions and the speed of convergence connected with an increase in the stability with respect to noisy data. Proposed Newton reconstruction methods can be extended for reconstruction of perfectly electric conducting (PEC) objects located on known domain by using the fundamental solution of Helmholtz equation on known domain and its far field pattern and using the incident field as field in the absence of the PEC object. Fundamental solution of Helmoltz equation on known domain and Field in the absence of the PEC object are well known direct scattering problem. Proposed method can be easily extended for limited angular and near field measurements of scattered fields. Proposed method is described in detail and illustrated its feasibility through examples with exact and noisy data. [ABSTRACT FROM AUTHOR]