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This book explores cutting-edge techniques and algorithms at the intersection of sparse signal theory and high-frequency wireless communication. As terahertz (THz) systems become integral to 6G and beyond, they face challenges such as high path loss, limited hardware capabilities, and massive data rates. This book provides a comprehensive overview of how sparsity-based methods, including compressed sensing, sparse channel estimation, and dictionary learning, can effectively address these challenges. It delves into both theoretical foundations and practical implementations, covering aspects like beamforming, signal recovery, modulation, detection, and spectrum sensing in THz bands. Readers will gain insights into the integration of sparse models with machine learning and hardware-constrained platforms. Designed for researchers, engineers, and graduate students, the book bridges the gap between advanced signal processing and real-world THz system design, offering a roadmap to buildefficient, scalable, and energy-aware wireless communication solutions for the future.