Wavelets is a carefully organized collection of extended survey papers addressing key topics in the foundations and applications of wavelet theory. The first part of the book is devoted to the fundamentals of wavelet analysis. It covers the construction of wavelet bases and the fast computation of the wavelet transform in both continuous and discrete settings and presents the theory of frames, dilation equations, and local Fourier bases. The second part discusses applications in signal analysis, while the third part covers operator analysis and partial differential equations. While mathematically precise, this book is ideal for a general scientific and engineering audience.