This dissertation investigates novel applications of the wavelet transform in the analysis and compression of audio, still images, and video. In a second focal point, we evaluate the didactic potential of multimedia–enhanced teaching material for higher education. Most recently, some theoretical surveys have been published on the potential for a wavelet–based restoration of noisy audio signals. Based on these, we have developed a wavelet–based denoising program for audio signals that allows flexible parameter settings. It is suited for the demonstration of the potential of wavelet–based denoising algorithms as well as for use in teaching. The multiscale property of the wavelet transform can successfully be exploited for the detection of semantic structures in still images. For example, a comparison of the coefficients in the transformed domain allows the analysis and extraction of a predominant structure. This idea forms the basis of our semiautomatic edge detection algorithm that was developed during the present work. A number of empirical evaluations of potential parameter settings for the convolution–based wavelet transform and the resulting recommendations follow.