Abstarct: ‎This thesis examines the necessity of using wavelet methods in solving integral equations, especially focusing on their application in first order and higher order Fredholm, Volterra and Volterra-Frodhelm integro-differential equations. This study introduces a wavelet collocation method baxsed on multiple linear Legendre wavelets that uses the wavelet transform to increase the accuracy and efficiency of the solutions of these complex equations. The presented numerical method shows significant improvements over traditional methods in computational speed and accuracy. This research highlights the advantages of wavelet-baxsed methods in handling the challenges posed by integro-differential equations and provides a comprehensive analysis of their practical applications. The findings emphasize the effectiveness of wavelet methods and provide valuable insights into their role in advancing numerical analysis.‎