Data mining techniques have been widely applied to extract desirable knowledge from existing databases for specific purposes. In real-world applications, a database usually involves the time periods when transactions occurred and exhibition periods of items, in addition to the items bought in the transactions. To handle this kind of data, temporal data mining techniques are thus proposed to find temporal association rules from a database with time. Most of the existing studies only consider different item lifespans to find general temporal association rules, and this may neglect some useful information. For example, while an item within the whole exhibition period may not be a frequent one, it may be frequent within part of this time. To deal with this, the concept of a hierarchy of time is thus applied to temporal data mining along with suitable time granules, as defined by users. In this thesis, we thus handle the problem of mining temporal association rules with a hierarchy of time granules from a temporal database, and also propose three novel mining algorithms for different item lifespan definitions. In the first definition, the lifespan of an item in a time granule is calculated from the first appearance time to the end time in the time granule. In the second definition, the lifespan of an item in a time granule is evaluated from the publication time of the item to the end time in the time granule. Finally, in the third definition, the lifespan of an item in a time granule is measured by its entire exhibition period. The experimental results on a simulation dataset show the performance of the three proposed algorithms under different item lifespan definitions, and compare the mined temporal association rules with and without consideration of the hierarchy of time granules under different parameter settings.