arXiv:2602.21268v2 Announce Type: replace Abstract: Soft set theory provides a systematic framework for parameterized decision-making by associating each parameter with a subset of a given universe, thereby enabling structured representations of uncertainty [1, 2]. Over the past decades, the theory has evolved into a broad range of extensions, including hypersoft sets, superhypersoft sets, TreeSoft sets, bipolar soft sets, and dynamic soft sets, while also establishing connections with various mathematical disciplines, particularly topology and matroid theory. This book presents a comprehensive survey of soft set theory and its principal extensions, with particular emphasis on parameter spaces, value spaces, representative mathematical constructions, and the underlying assumptions necessary for rigorous comparisons among different frameworks. It carefully distinguishes established definitions from the literature from exploratory formulations and critically examines the limitations of selected claims concerning representation and reduction. Building upon the first edition, this second edition introduces additional concepts and illustrative examples, addresses previously identified mathematical inconsistencies and typographical errors, and refines the overall structure and presentation to enhance mathematical rigor, clarity, and readability.