Preface 1. Preliminaries 1.1. Short LMS Algorithm History 1.2. Random Processes 1.3. Stability and Convergence 1.4. Linear Optimum Filtering 1.5. Least MEan Squares Algorithm 1.6. Partial Update Algorithms 2. Classic Stability and Convergence Analysis 2.1. Introduction 2.2. Small-Step-Size Theory 2.3. Independence Theory 2.4. Stability of Modified LMS Algorithms 2.5. Stability of Partial Update LMS Algorithms 3. Control Theory-Based LMS Algorithm Stability Analysis 3.1. Stability of LMS Algorithm 3.2. Stability of Leaky LMS Algorithm 3.3. Weak Stability Condition for Partial Update LMS Algorithms 4. LMS Algorithm Applications 4.1. Introduction 4.2. System Identification 4.3. Acoustic Echo Cancellation 4.4. Adaptive Line Enhancer 4.5. Active Noise Control 4.6. Conclusions 5. Summary A. Mathematics Applied in this Monograph B. Main Control Theory Theorems References Nomenclature Index