class

The root class comes from Latin classis, and to understand the whole family you have to picture ancient Rome on census day. According to tradition, the king Servius Tullius divided the citizens into property groups so the state would know who could afford armor and who could only carry a sling. Each of these property tiers was a classis — a 'rank' or 'division' of the people. The richest were in the first classis; everyone too poor to be ranked was literally 'below class,' infra classem, which is where our word 'infraclass'-style thinking and even the idea of being 'beneath one's class' begins.

Notice that classis was never about books or schools at first. It was about sorting people by status. That single idea — putting things into ranked groups — is the seed of every modern sense.

- A class is still a group sharing some feature. Roman social ranks became the modern social class (upper class, working class). The 'group of people sorted together' sense slid naturally into the schoolroom: a class is the batch of students grouped by year. From there English took one more step — the lesson that group attends became 'a class' too ('I have a math class at noon'). And because the top Roman classis was the best one, 'class' picked up the admiring sense of quality: a person 'with class,' a 'classy' restaurant.
- classic = belonging to the highest class. The Romans called their best writers scriptores classici, 'first-class authors,' worth studying as models. So a classic is anything of proven, top-rank quality — a classic novel, a classic mistake (the textbook, model example of a mistake).
- classical narrowed the same idea to a specific top rank: the culture of ancient Greece and Rome (classical antiquity, classical languages), and by extension the formal European art-music tradition built on those ideals (classical music, as opposed to pop or jazz).
- classify / classification add the Latin verb facere ('to make'): to classify is literally to 'make into classes,' to sort things into ranked groups. The noun classification is that act or its result — biological classification, a security classification.
- classmate / classroom keep the schoolroom sense: the people in your class, and the room where the class meets.

One hidden branch is worth knowing: in Latin, classis also meant a fleet — a 'called-up' assembly of warships (it is related to calare, 'to call/summon,' the same idea behind 'a group summoned together'). That military sense barely survives in English, but it explains the underlying logic of the whole family: a class is fundamentally a body of people or things called together and ranked. Whether it is a fleet, a social rank, or a row of students, the picture is the same — a group sorted out and lined up.