The trivium is implicit in De nuptiis Philologiae et Mercurii ("On the Marriage of Philology and Mercury") by Martianus Capella, but the term was not used until the Carolingian Renaissance, when it was coined in imitation of the earlier quadrivium. Grammar, logic, and rhetoric were essential to a classical education, as explained in Plato's dialogues. The three subjects together were denoted by the word trivium during the Middle Ages, but the tradition of first learning those three subjects was established in ancient Greece. Contemporary iterations have taken various forms, including those found in certain British and American universities (some being part of the Classical education movement) and at the independent Oundle School in the United Kingdom.
Etymologically, the Latin word trivium means "the place where three roads meet" (tri + via); hence, the subjects of the trivium are the foundation for the quadrivium, the upper division of the medieval education in the liberal arts, which consists of arithmetic (numbers as abstract concepts), geometry (numbers in space), music (numbers in time), and astronomy (numbers in space and time). Educationally, the trivium and the quadrivium imparted to the student the seven liberal arts of classical antiquity.
Grammar teaches the mechanics of language to the student. This is the step where the student "comes to terms," defining the objects and information perceived by the five senses. Hence, the Law of Identity: a tree is a tree, and not a cat.
Logic (also dialectic) is the "mechanics" of thought and of analysis, the process of composing sound arguments and identifying fallacious arguments and statements and so systematically removing contradictions, thereby producing factual knowledge that can be trusted.
Rhetoric is the application of language in order to instruct and to persuade the listener and the reader. It is the knowledge (grammar) now understood (logic) and being transmitted outwards as wisdom (rhetoric).
Sister Miriam Joseph, in The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric (2002), described the trivium as follows:
Grammar is the art of inventing symbols and combining them to express thought; logic is the art of thinking; and rhetoric is the art of communicating thought from one mind to another, the adaptation of language to circumstance.
. . .
Grammar is concerned with the thing as-it-is-symbolized. Logic is concerned with the thing as-it-is-known. Rhetoric is concerned with the thing as-it-is-communicated.
John Ayto wrote in the Dictionary of Word Origins (1990) that study of the trivium (grammar, logic, and rhetoric) was requisite preparation for study of the quadrivium (arithmetic, geometry, music, and astronomy). For the medieval student, the trivium was the curricular beginning of the acquisition of the seven liberal arts; as such, it was the principal undergraduate course of study. The word trivial arose from the contrast between the simpler trivium and the more difficult quadrivium.
- Onions, C.T., ed. (1991). The Oxford Dictionary of English Etymology. p. 944.
- Marrou, Henri-Irénée (1969). "Les arts libéraux dans l'Antiquité classique". pp. 6–27 in Arts libéraux et philosophie au Moyen Âge. Paris: Vrin; Montréal: Institut d'études médiévales). pp. 18–19.
- See Martin Robinson, Trivium 21st century. Each of these iterations was discussed in a conference at King's College London on the future of the liberal arts at schools and universities; see  and Boarding Schools Association,Oundle School - improving intellectual challenge.
- Taylor, Thomas (1811). The Rhetoric, Poetic and Nicomachean Ethics of Aristotle. London: Robert Wilks. p. 6.
- Joseph, Sister Miriam (2002). "1, The Liberal Arts". The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric. Paul Dry Books. pp. 3, 9. ISBN 9781589882737.
- Ayto, John (1990). Dictionary of Word Origins. University of Texas Press. p. 542. ISBN 1-55970-214-1.
- McLuhan, Marshall (2006). The Classical Trivium: The Place of Thomas Nashe in the Learning of His Time. (McLuhan's 1942 doctoral dissertation.) Gingko Press. ISBN 1-58423-067-3.
- Michell, John, Rachel Holley, Earl Fontainelle, Adina Arvatu, Andrew Aberdein, Octavia Wynne, and Gregory Beabout. "Trivium: The Classical Liberal Arts of Grammar, Logic, & Rhetoric. New York: Bloomsbury, 2016. Print. Wooden Books".
- Robinson, Martin (2013). Trivium 21c: Preparing Young People for the Future with Lessons from the Past. London: Independent Thinking Press. ISBN 978-178135054-6.
- Sayers, Dorothy L. (1947). "The Lost Tools of Learning". Essay presented at Oxford University.
- Winterer, Caroline (2002). The Culture of Classicism: Ancient Greece and Rome in American Intellectual Life, 1780–1910. Baltimore: Johns Hopkins University Press.