The Broad Learning System proposes a novel machine learning approach which emphasizes efficiency, flexibility, and simplicity. As opposed to traditional deep learning models, which rely on deep layered architecture and iterative training, BLS employs shallow, horizontally extensible architecture. BLS has drawn great research attention in a wide range of fields, including image classification, biomedical signal processing, gesture recognition, and fault diagnosis. This book provides a comprehensive overview of BLS, including its structure, mathematics, recent advances, and implementations in the real world. Furthermore, we present some promising avenues for future research, including the design of hybrid BLS architectures, techniques for enhanced noise robustness, and their potential integration into edge computing platforms. BLS was found to be a promising prospect for real time learning issues, especially in resource constrained settings where model interpretability and high speed are of utmost significance.