The ICM Methodology provides a definitive framework for structural topology optimization, integrating solid mechanics, mathematical programming, and advanced structural design. This monograph presents the Independent, Continuous, and Mapping (ICM) method, focusing on the approximation of hurdle functions to solve complex engineering challenges. It delivers technical depth on multi-material and fail-safe optimization, reciprocal programming, and node-uncoupling approaches. By progressing from foundational theory to explicit modeling, the book provides a systematic strategy for managing gray elements and achieving clear structural configurations.This book encapsulates years of dedicated research by the authors' team, documenting the definitive transition of the ICM approach from the method stage to a mature, rigorous methodology. Readers will benefit from included program codes and practical examples, enabling the immediate application of ICM theory to real-world, multi-load case engineering projects. Practitioners in mechanical, aerospace and civil engineering will gain the ability to design high-performance, weight-efficient structures that meet rigorous stress and displacement constraints.