An elementary school or primary school is an institution where children receive the first stage of compulsory education known as elementary or primary education. Elementary school is the preferred term in some countries, particularly those in North America, where the terms grade school and grammar school are also used. Primary school is the preferred term in the United Kingdom, India, Ireland, Pakistan, Bangladesh, Australia, Latin America, Nepal, South Africa, New Zealand, Malaysia and in most publications of the United Nations Educational, Scientific, and Cultural Organization (UNESCO).

Elementary school was formerly the name given to publicly funded schools in Great Britain which provided a basic standard of education for working class children aged from five to 14, the school leaving age at the time. They were also known as industrial schools.

Elementary schools were set up to enable working class children to receive manual training and elementary instruction. They provided a restricted curriculum with the emphasis on reading, writing and arithmetic (the three Rs). The schools operated on a 'monitorial' system, whereby one teacher supervised a large class with the assistance of a team of monitors, who were quite often older pupils. Elementary school teachers were paid by results. Their pupils were expected to achieve precise standards in reading, writing and arithmetic such as reading a short paragraph in a newspaper, writing from dictation, and working out sums and fractions.