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The Method of Moments (MoM) has been used extensively to solve electromagnetic problems. Its popularity is largely attributed to its adaptability to structures with various shapes and success in predicting the equivalent induced currents accurately. However, due to its dense matrix, especially for large structures, the MoM suffers from long matrix solution time and large storage requirement. In this thesis it is shown that use of wavelet basis functions result in a MoM matrix which is sparser than the one obtained by using traditional basis functions. A new wavelet system, different from the ones found in literature, is proposed. Stabilized Bi-Conjugate Gradient Method which is an iterative matrix solution method is utilized to solve the resulting sparse matrix equation. Both a one-dimensional problem with a microstrip line example and a two-dimensional problem with a rectangular patch antenna example are studied and the results are compared.