"Ü", or "ü", is a letter, representing a vowel, in the Estonian, Hungarian, and Turkish alphabets. It also appears in the German alphabet, where it represents "U" with umlaut, and is alphabetized together with "U". This letter also appears in Swedish for German names (where it's alphabetized together with "Y"), and in Dutch both for German names and for words that came originally from German. It's also used in Spanish writing.
In Spanish and Catalan "Ü" is the letter "U" with a diaeresis, indicating that "U" is pronounced in a position where it would not normally be, specifically between a "G" and an "E" or "I" in Spanish and Catalan and between a "Q" and "E" or "I" in Catalan
Since in Spanish the pronunciation of "G" changes from /g/ to /x/ (same as "J") when followed by "I" or "E" (vocales débiles, weak vowels), a silent "U" can be added after it to restore the /g/ sound. For example, guerra (war) is pronounced /geRa/, not /xeRa/. If the "U" is to be pronounced, then a diaeresis is added; for example, lingüistica (linguistics) is pronounced /lingwistika/, not /lingistika/. Similarly, in Catalan.
Another use exclusive of Catalan language consist into separate two vowels that without the diaeresis would sound together in the same syllable. For example diurn would sound /djwrn/ but diürn sounds /di'urn/ (two syllables).
In the Chinese romanizations pinyin, Wade-Giles, and the German-based Lessing-Othmer, "Ü" is used to represent the vowel of 玉 (jade) and 雨 (rain). Pinyin uses "Ü" only when ambiguity could arise, while Wade-Giles and Lessing use it in all situations.