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Wavelet theory was an active area of research in mathematics when this book was first published, but I'm unable to find any mention of the use of wavelets in the book's table of contents.

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In terms of an introductory DSP guide, wavelets aren't all that fundamental compared to eg filters, impulse/frequency responses, and the DFT, unless you're working specifically with something like image compression.

Aren't wavelets analogous to the fourier transform. Wouldn't that mean it would be a fundamental aspect of DSP these days?

True, the Fourier transform can be viewed as a specialization of wavelet transforms, so in that sense wavelets are fundamental. Like many mathematical subjects the specialization is treated before some historical generalization in educational contexts (if the generalization is ever discussed, as it doesn't seem to be here). Practically speaking, while wavelet theory is fascinating, you can get plenty of DSP done without knowing it; but not having some understanding of the DFT is crippling.

There is actually a similarly written book for wavelets. Conceptual Wavelets in Digital Signal Processing http://a.co/5rspz0i

Nice. D. Lee Fugal is also a co-author of The Essential Guide to Digital Signal Processing (2014):

https://www.amazon.com/Essential-Guide-Digital-Signal-Proces...

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