Abstract: In this talk, we will define and give examples of multiresolution analysis. In particular we develop the Haar and Daubechies families of scaling functions and wavelets. We then discuss the Mallat algorithm for the fast wavelet transformation. As an application of wavelet analysis we consider Magnetic Resonance Imaging. Due to their localization in space, wavelet encoding has two distinct advantages over the traditional Fourier encoding. The first of these is a reduction in motion artifacts while the second is a decrease in imaging time.