A primary school (in Ireland, India, the United Kingdom, Australia, New Zealand, Trinidad and Tobago, Jamaica, Nigeria, South Africa, and Singapore), elementary school, or grade school (in North America and the Philippines) is a school for primary education of children who are 4 to 10 years of age (and in many cases, 11 years of age). Primary schooling follows preschool and precedes secondary schooling.

The International Standard Classification of Education considers primary education as a single phase where programmes are typically designed to provide fundamental skills in reading, writing, and mathematics and to establish a solid foundation for learning. This is ISCED Level 1: Primary education or first stage of basic education.

The word phrase "primary school" is a calque from French école primaire, which was first used in a text of London Times in April 1802.

In most parts of the world, primary education is the first stage of compulsory education, and is normally available without charge, but may also be offered by fee-paying independent schools. The term grade school is sometimes used in the US, although both this term and elementary school may refer to the first eight grades, in other words both primary education and lower secondary education.

In the United Kingdom, "elementary education" was taught in "elementary schools" until 1944, when free elementary education was proposed for students over 11: there were to be primary elementary schools and secondary elementary schools; these became known as primary schools and secondary schools.

Although often used as a synonym, "elementary school" has specific meanings in different locations.

In Chinese-speaking world except of Taiwan, the Chinese word xiǎo xué (simplified Chinese: 小学; traditional Chinese: 小學) is used. 國小 is only used in Taiwan.

In older texts it can mean linguistics including phonology, grammatology and semantics.