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The Decision Model and Notation (DMN) is a standard notation to capture decision logic in business applications. A central construct in DMN is that of a decision table. The increasing use of DMN decision tables to capture critical business knowledge raises the need to support analysis and refactoring tasks on these tables. This article puts forward a formal semantics for DMN decision tables and a formal definition of analysis tasks on such tables. The article then proposes a general approach to analyze and refactor decision tables based on a geometric interpretation thereof. This general approach is used to design efficient algorithms for two analysis tasks (detection of overlapping rules and of missing rules) and one refactoring task (simplification of tables via rule merging). The algorithms have been implemented in an open-source DMN editor and tested on large decision tables derived from a credit lending dataset.