学校【がっこう】
school
大学【だいがく】
university, college, former imperial university of Japan (established under the ritsuryō system for the training of government administrators), the Great Learning (one of the Four Books)
学ぶ【まなぶ】
to study (in depth), to learn, to take lessons in
学生【がくせい】
student (esp. a university student)
科学【かがく】
science
学園【がくえん】
educational institution, school, academy, campus
科学者【かがくしゃ】
scientist
学生【がくしょう】
Heian-period student of government administration, Buddhist scholar, researcher at a Buddhist temple, person studying Buddhism, learning, scholarship
中学【ちゅうがく】
junior high school, middle school, lower secondary school
小学校【しょうがっこう】
primary school, elementary school, grade school
入学【にゅうがく】
admission (to a school or university), entrance, enrolment, enrollment, matriculation
見学【けんがく】
inspection, study by observation, field trip, tour, review, sitting out (e.g. PE class)
数学【すうがく】
mathematics
小学生【しょうがくせい】
elementary school student, primary school student, grade school student
退学【たいがく】
dropping out of school, withdrawal from school, expulsion from school, dismissal, leaving school (university, etc.) after completing a course
中学生【ちゅうがくせい】
junior high school student, middle school pupil
医学【いがく】
medical science, medicine
大学生【だいがくせい】
university student, college student
学者【がくしゃ】
scholar, academic, scientist, learned person, person of learning
留学【りゅうがく】
studying abroad, (temporarily) studying at another school (to learn a specific skill)