Adaptive filters with a large number of coefficients are usually involved in both network and acoustic echo cancellation. Consequently, it is important to improve the convergence rate and tracking of the conventional algorithms used for these applications. This can be achieved by exploiting the sparseness character of the echo paths. Identification of sparse impulse responses was addressed mainly in the last decade with the development of the so-called ''proportionate''-type algorithms. The goal of this book is to present the most important sparse adaptive filters developed for echo cancellation. Besides a comprehensive review of the basic proportionate-type algorithms, we also present some of the latest developments in the field and propose some new solutions for further performance improvement, e.g., variable step-size versions and novel proportionate-type affine projection algorithms. An experimental study is also provided in order to compare many sparse adaptive filters in different echo cancellation scenarios. Table of Contents: Introduction / Sparseness Measures / Performance Measures / Wiener and Basic Adaptive Filters / Basic Proportionate-Type NLMS Adaptive Filters / The Exponentiated Gradient Algorithms / The Mu-Law PNLMS and Other PNLMS-Type Algorithms / Variable Step-Size PNLMS Algorithms / Proportionate Affine Projection Algorithms / Experimental Study