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This dissertation is about adversarial, case-based reasoning and the HYPO program that performs adversarial reasoning with cases and hypotheticals in the legal domain. The dissertation identifies and describes basic case-based operations, an adversarial, case-based reasoning process, a schematic structure for case-based arguments, the kinds of counter-examples that arise and the knowledge sources necessary to support adversarial, case-based reasoning. The HYPO program embodies the methodology. It comprises: (1) a structured Case Knowledge Base (CKB) of actual legal cases; (2) an indexing scheme (dimensions) for retrieval of relevant cases from the CKB; (3) methods for analyzing problem situations and retrieving relevant cases; (4) methods for interpreting and assessing the relevancy of past cases by positioning the problem situation with respect to relevant existing cases in the CKB as seen from the viewpoint of the problem at hand and finding the most-on-point cases; (5) methods for comparing/contrasting cases (e.g., citing, distinguishing, finding counter-examples); (6) methods for posing hypotheticals that test the sensitivity of the problem situation to changes, particularly with regard to potentially adverse effects of new damaging facts coming to light and existing favorable ones being discredited; (7) methods for generating 3-ply argument outlines to play out realistic legal arguments citing cases in a manner familiar to attorneys; and (8) methods for explaining alternative decisions of the problem situation by posing hypotheticals, comparing arguments and summarizing the precedents. HYPO's performance compares favorably to that of judges and attorneys in actual legal cases. The law is an excellent domain to study case-based reasoning since by its very nature it: (1) espouses a doctrine of precedent in which prior cases are the primary tools for justifying legal conclusions; and (2) employs precedential reasoning to make up for the lack of strong domain models with which to reason deductively about problem situations. The law is also a paradigm for adversarial case-based reasoning; there are no right answers, only arguments pitting interpretations of cases and facts against each other. The dissertation addresses issues of central concern to Artificial Intelligence including: relevance and credit assignment, indexing and inference control, argumentation, analogical reasoning and explanation.