United Kingdom
In the United Kingdom, unlike the United States, students do not usually 'graduate' from school below university level. They will normally leave secondary school and sixth form college (if applicable) with specific qualifications, often GCSEs and A-levels respectively (Standard Grades and Higher National Courses in Scotland). However, these are not diplomas and are not necessarily presented in a formal ceremony.
Many university graduation ceremonies in the United Kingdom begin with a procession of academics, wearing academic dress. This procession is accompanied by music, and a ceremonial mace is often carried. However, Pomp and Circumstance is not played, since this is a patriotic hymn. After this, an official reads out the names of the graduates one by one, organized by class of degree or by subject. When their names are called, the graduates walk across the stage to shake hands with a senior official, often the university's nominal Chancellor or the vice-chancellor.
Graduates wear the academic dress of the degree they are receiving. Serving members of the armed forces may wear their military uniform underneath.
Some of the older universities may hold their graduation ceremonies in Latin, whilst member institutions of the University of Wales hold their graduation ceremonies almost entirely in the Welsh language, even though few students understand either of these languages.
The Latin section of the ceremony may include a rendition of an anthem, sometimes called the unofficial anthem of all universities, the De Brevitate Vitae, also known as The Gaudeamus.
Source: Wikipedia, the free encyclopedia

