Short answers, pulled from the story.
A gymnasium is a type of secondary school in Europe that prepares academically selected students for university. It differs from a general high school in that admission is competitive, typically occurring between ages 10 and 13, and the curriculum includes Latin, Ancient Greek, and multiple foreign languages alongside standard academic subjects.
The word gymnasium derives from the ancient Greek gumnasion, rooted in gumnos meaning naked, referring to the athletic grounds of ancient Athens where teachers also instructed young men. The educational meaning was revived during the Renaissance in Italy and spread into the Netherlands and Germany during the 15th century.
Johannes Sturm founded the school at Strasbourg in 1538 that became the model for the modern German gymnasium. A Prussian regulation in 1812 then required all schools with the right to send students to university to formally carry the name gymnasium.
Depending on the country, the final exam is called the Abitur, Matura, Maturita, Artium, Diploma, or Student. In Germany, the final Abitur examinations are centrally drafted in all states except Rhineland-Palatinate and qualify students to attend any German university.
The four traditional branches are humanities, specializing in classical languages such as Latin and Greek; modern languages, requiring at least three languages; mathematics and physical sciences; and economics and social sciences, covering world history, economics, and business informatics.
Grammar schools were historically the English equivalent of the gymnasium, selecting pupils through the 11+ entrance examination. They were largely phased out from 1965 under the Wilson and Heath governments, and today fewer than 5% of pupils attend the remaining 146 grammar schools, mainly in Northern Ireland, Buckinghamshire, Lincolnshire, and Kent.