《周易》本為卜筮之書，以大衍之數作為天地自然之定數，表徵陰陽的變化，萬理萬象皆因之以立，萬事萬物之代謝變遷、紛紜交錯，皆因之以全。透過「數」的操作運式所建構的占筮之法，一切的存在與現象，一切的吉凶休咎，都在大衍之數的運作下確定。大衍之學隨著宋代圖書易學與對數論的重視，成為宋代易學的重要標誌，而張理的圖書易學與大衍筮法的推布，在宋元之際具有承先啟後的地位。本文以張理的大衍筮法作為研究論題，主要從大衍與河洛之法的關係、用數之本及合天圓地方之義等幾個重要衍學觀點為探述起點，進而論釋大衍揲蓍之法，以及變占之原則與通例，藉由詳細而系統化的疏理，申明其大衍學的實質內涵與所傳達的重要意義。

Zhouyi is a book of divination, with Dayan numbers, the fixed numbers of heaven, earth, and nature, symbolizing the change of Yin and Yang. Changes of things can never be complete without Dayan numbers. With the divination developed through the use of numbers, all existences, phenomena, auspices and omens are determined under the practice of Dayan numbers. Dayan theory became an important feature in Yixue in the Song Dynasty since Tu-Shu Yixue at that time put emphasis on numbers. Zhang Li’s Tu-Shu Yixue and his application of Dayan divination eared himself a significant position in the Yixue history in Yuan Dynasty. With the focus on divination, the present study aims to provide a detailed and systematic analysis of Zhang’s theory of Dayan divination, explain the relationship between Dayan and Hetu and Luoshu, the significance of the number 49 used in the concept of “heaven round and earth square”, and principles of Bian-zhan, alternation divination, and further explore the essence of Zhang’s Danya theory and the meanings it conveys.