Introduction to wavelets?

The canonical answer used to be Ingrid Daubechies, Ten lectures on wavelets (1992), ISBN 0898712742. It may be somewhat outdated by now, but probably still good.

In a course on Fourier Analysis, we used Fourier Analysis and Applications by Gasquet and Witomski (translated by Ryan). The subtitle is "Filtering, Numerical Computation, Wavelets". The wavelets section is one chapter at the end so it doesn't go into much detail specifically on wavelets. So if you already know a lot of Fourier analysis then I wouldn't use this book, but if you also need to know the Fourier analysis background then it's a reasonable place to start. It's quite readable as well.

Refs:

• ISBN: 0-387-98485-2
• Publisher: Springer, Texts in Applied Mathematics 30
• MathSciNet: MR1657104 (includes review)

I think "Ripples in Mathematics: The Discrete Wavelet Transform" by Arne Jensen and Anders la Cour-Harbo (Springer 2001) is a masterpiece of elegant exposition. You can find it here. I learned more about wavelets from this book than from any other source.