Abstract : This thesis is devoted to the numerical resolution of weakly singular Fredholm equations of second kind posed on a Banach space. The methods which are described are applied more specifically in the case of the space of continuous functions on a compact interval, and in the case of Lebesgue integrable functions on a compact interval. The first chapter briefly gives the theoretical framework of this study. Different kinds of convergence of a sequence of operators in a complex Banach space are recalled, and so are their properties. The second chapter is devoted to the description and the to analysis of two finite rank approximate methods. Three refinement schemes are applied to these methods. Relative error bounds are given, for each method and in the case of each functional space. Convergence rate of each corresponding refinement scheme is also deduced. A detailed description of the implementation of these schemes is given. The third chapter deals with the application of these methods to the resolution of the transfer equation. This equation appears in a wider problem (which comes from the transfer theory). A brief description of this problem is given in the case of the particular framework of stellar atmospheres. Numerical experiments are presented. They deal with the validation of the proposed methods and with some astrophysical meaningful cases. When the integral parameter is very large, which is the case in some astrophysical problems, the numerical resolution of this equation is difficult. So, the end of this chapter is devoted to the description of asymptotical domain decomposition methods which can be efficient to overcome this difficulty.