In seismic analysis and other areas of the geosciences, wavelet analysis is superior to the signal processing governed by the theory of Fourier transformation because it is more valuable in understanding deviation from time and space statistical properties. Developed from a graduate course on wavelets held at the Department of Geomatics Engineering at the U. of Calgary (Canada), this textbook mathematically develops wavelet theory as applied in digital signal processing. Definitions and results are given in a mathematically rigorous form, while proofs are kept comparatively short. The reader is assumed to have a graduate-level mathematics education.