An Introduction to Wavelets is the first volume in a new series, Wavelet Analysis and Its Applications. This is an introductory treatise on wavelet analysis , with an emphasis on spline-wavelets and time-frequency analysis. Among the basic topics covered in this book are time-frequency localization, integral wavelet transforms, dyadic wavelets, frames, spline-wavelets, orthonormal wavelet bases, and wavelet packets. In addition, a unified treatment of nonorthogonal, semiorthogonal, and orthogonal wavelets is presented. This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis. It is suitable as a textbook for a beginning course on wavelet analysis and is directed toward both mathematicians and engineers who wish to learn about the subject. Specialists may use this volume as supplementary reading to the vast literature that has already emerged in this field.