This chapter presents some basic approaches of wavelets for the solution of partial differential equations. The concept of spaces is necessary for proper understanding of wavelets but for simplicity, the strenuous concept of functional analysis is avoided in the beginning. The chapter also presents essential concepts of wavelets in a simple way. Wavelets are most widely used in signal and image processing because of their efficient low and high pass filtering algorithms. Wavelets offer many interesting techniques to solve various types of differential equations because of their multiresolution character, spectral nature, high and low frequency components, compact support, orthogonal and vanishing moment properties. Wavelet-Galerkin method is very similar to the finite element method and appears to be more useful than the collocation method for engineering problems.