Image processing in hexagonal grid is very much advantageous than in the conventional rectangular grid. The advantages include higher angular resolution, consistent connectivity and higher sampling efficiency. A wide class of operations on images can be performed directly in the wavelet domain by operating on its coefficients of the images. Operating in wavelet domain enables to operate on different resolutions, manipulate features at different scales and localize the operation in both spatial and frequency domains. Many multiresolution image processing operations becomes faster and more efficient if it is done in wavelet domain. Hexagonal wavelet includes the advantages of the hexagonal grid along with the wavelets which will be very useful in multiresolution operations. A new method of designing hexagonal wavelets using lifting scheme in the spiral addressing scheme is proposed in this book. It is computationally efficient because they are not based on Fourier transforms, and could be performed in place.