A complete description is given for the algorithms in S+Wavelets software toolkit for wavelet and cosine packet analysis. These algorithms include wavelet transforms, wavelet packet transforms, cosine packet transforms, and non-decimated wavelet transforms. Implementations for the transforms and their inverses are given for a variety of boundary treatment rules, including periodic, reflection, interval wavelets (Cohen et al. [CDV93]), and zero/polynomial extension. In addition, modifications to the standard algorithms are given to handle signals or images with dimensions not divisible by a power of two. Keywords: Discrete wavelet transform, discrete cosine transform, wavelet packet transform, boundary rules, algorithms, S+WAVELETS. 1 1 Introduction This paper describes the algorithms in the S+Wavelets toolkit for the wavelet and cosine packet analysis. S+Wavelets is an S-PLUS module for wavelet analysis of signals and images. See Bruce and Gao [BG94, BG95] for details concerning th...