Are there any suggestions for introductory books on wavelets? I want a book, not online material or tutorials.

$\begingroup$ Mallat's book is possibly the only correct answer to this question :D (..I have done 2 courses which covered parts of this book!..) $\endgroup$ – gradstudent Apr 12 '18 at 23:33
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 It may be somewhat outdated by now, but probably still good.

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$\begingroup$ I haven't looked this stuff in years, but my recollection is that the writings of Daubechies and Mallat are all quite readable. $\endgroup$ – Deane Yang Feb 8 '10 at 3:12
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: 0387984852
 Publisher: Springer, Texts in Applied Mathematics 30
 MathSciNet: MR1657104 (includes review)

$\begingroup$ I hope you don't find me annoying for saying so, but you should have retagged the question when you posted this answer. $\endgroup$ – Anton Geraschenko Nov 10 '09 at 15:15

$\begingroup$ I'll see your "retag" and raise you a "edit to make community wiki". (Seriously; no, I don't find you annoying for saying so. I forgot that I have such SuperPowers.) $\endgroup$ – Loop Space Nov 10 '09 at 15:48
I think "Ripples in Mathematics: The Discrete Wavelet Transform" by Arne Jensen and Anders la CourHarbo (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.
A very gentle introduction is Boggess & Narcowich, A First Course in Wavelets with Fourier Analysis. I should warn you, though, they're pretty fast and loose with the hypotheses of their theorems. You'll be fine if you've studied advanced linear algebra, and especially fine if you already know some Fourier analysis.
There's also Mallat's A Wavelet Tour of Signal Processing: The Sparse Way. I haven't read very much of it, so I don't have a strong opinion on it yet. It's definitely more difficult than Boggess & Narcowich, but then it probably has about ten times the content (no exaggeration).
A Primer on Wavelets and Their Scientific Applications by James S. Walker
Real Analysis with an Introduction to Wavelets and Applications by Hong, Wang and Gardner
All The Mathematics You Missed recommends The World According to Wavelets by Barbara Burke Hubbard. I haven't read it myself, though.
When I started out on wavelets, I really liked "Wavelets: A Primer" by Christian Blatter (ISBN: 1568810954) which is pretty selfcontained in that it even contains a thorough review of the Fourier analysis used. It seems to be out of print, unfortunately.
Let me mention Mark Pinsky’s book, “Introduction to Fourier transform and wavelets”.
(I am wondering if the book is too much math for engineering people?)

$\begingroup$ @ChrisRamsey it's weirdly stated (fixed in my edit), but like the other answers it's a book suggestion, so I wouldn't say it does not provide an answer. The relevance/usefulness of such a list (esp. with no or few comments) is another problem... $\endgroup$ – YCor Apr 12 '18 at 21:02
