This book presents a novel Cross-Layer Approximation and Distribution architecture and methodology that advances the design of high-performance, high-throughput, energy-efficient, and sustainable reconfigurable computing systems. By leveraging the error tolerance inherent in modern AI and signal processing workloads, it enables performance and energy gains across hardware and software layers. The authors introduce innovative approximate multipliers, dividers, and coarse-grained processing elements for FPGA and CGRA platforms, coupled with an error-resiliency analysis and a heuristic-driven optimization framework that dynamically balance performance and accuracy. Extending beyond conventional architectures, the methodology described also integrates novel In-Network Computing (INC) techniques to bring computation closer to data sources within 5G/6G infrastructures. The result is a cohesive, scalable approach that redefines how energy-efficient and adaptive computing can be achieved across the edge-to-cloud continuum. Describes a unified perspective on how approximation techniques can be applied across multiple abstraction levels; Discusses how FPGAs, CGRAs and In-Network Computing can enable scalable, distributed, and low-latency computation; Introduces architectural designs such as approximate multipliers, dividers, and hybrid SIMD/MIMD processing elements.