The Hernandez-Weiss book is a great source in mathematics, where the reader can learn about
some fundamental and timeless tools of wavelet analysis. The presentation is clear and self contained. The book is great for an upper level analysis course, as well as for self study. Its emphasis is centered around the
multiresolution method, and it has both the basics in the subject, and
some exciting new results,-- those due
to the co-authors, as well as those of the analysts in the extended "Wash U-family" of researchers. It has a wealth of new material that
came after the 1992 classic of I. Daubechies ("Ten lectures on wavelets" SIAM ).The presentation in Hernandez-Weiss of, for example,
multiplicity theory and the dimension function is great for
the student who wishes to pick up the central ideas, or to
learn the details, step by step. The book contains both history and
motivation, and it points the reader towards a variety of exciting and timeless applications.