UT Libraries (and about all the libraries in North America) follow Library of Congress Chinese Romanization and Word Division rules.
Han yu pin yin 漢語拼音 (also called pinyin) is the romanizaion rule used in catalogs of North American libraries.
Wade-Giles romanization are still found used in older books and many old reference books.
For detail, see Library of Congress Chinese romanization and word division rules
Note: Wade-Giles was the romanization system used in the North American Libraries and the many publications before 2000.)
Wade-Giles, Zhu yin fu hao, pinyin in Wade-Giles order
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