I have been looking for the original of Cistercian Hymn''Jesu dulcis memoria'', which is possibly composed by St.Bernard. Do you know which medieval manuscript I can find this? Which library has the book? Am I able to get it from online, like a digital codex?
I wouldn't be surprised. It's not something likely to have been digitized. Old manuscripts generally would cost a lot of money to do that, given the conservation considerations. Old music, even in printed form, does not have a large online representation in the form of early editions, and I doubt it it will for many years to come. You'd have to research this the old-fashioned way - through specialized libraries. At least you can search for those online.
John Julian's venerable "Dictionary of Hymnody" (New York: Scribner's, 1892; p. 585ff. and p. 1537 - on Google Books) lists the medieval manuscripts where it can be found. According to Julian, the earliest MS dates from the end of the 12th century and has 42 (!) verses.(Later MSS added to this total.) There's also a discussion of some of textual variants in some of the MSS. However, the 1914 Catholic Encyclopedia states that Dom Pothier "found it in a manuscript of the eleventh century ascribed to a Benedictine abbess (St. Bernard was born in 1090)."
I don't know if any the MSS listed are available in facsimile - chances are they're not. You could check at the "Digital Image Archive of Medieval Music":
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