Compactly supported wavelet bases are sets of compactly supported functions that are orthonormal bases for a wide variety of function spaces, including signals that have finite energy or finite power. The theory of compactly supported wavelets is placed in its historical context. Wavelet matrices and wavelet functions of one and two variables are defined. The continuous, discrete, and finite wavelet transforms are contrasted with the corresponding Fourier transforms. A multirate digital filter interpretation is provided, and adaptive trees of wavelet filters are described.