A primary school (from French école primaire) is an institution in which children receive the first stage of compulsory education known as primary or elementary education. Primary school is the preferred term in the United Kingdom and many Commonwealth Nations, and in most publications of the United Nations Educational, Scientific, and Cultural Organization (UNESCO). In some countries, and especially in North America, the term elementary school is preferred. Children generally attend primary school from around the age of four or five until the age of eleven or twelve.
In Australia, Primary School is generally for children aged 5–12. In South Australia, Western Australia and Queensland grade 7 is part of primary school; in other states it forms part of secondary education. In certain year groups, students in all schools take part in the National Assessment Programme (NAP). The year levels:
Only in Queensland, South Australia and Western Australia the seventh year of education is considered part of "primary shool". The rest of Australia considers "primary school" only from years one through six. 
After primary school, students move on to high school.
Depending on State of Germany primary schools provide Education from Class 1 to Class 4 or from Class 1 to Class 6. After primary school students may attend a Hauptschule, a Realschule, a Gymnasium, a Intermediate School or a Gesamtschule.
In Hong Kong, students attend primary schools for the first six years of compulsory education.
In Ireland children aged between 4-5 years begin attending primary school with Junior Infants. There are eight different 'grades'. Participation is compulsory. This is the first of 14 prescribed years of formal education from a standardised curriculum set by the Department of Education.
In Malaysia, the first six years of education take place in primary schools. A standardized test is given to all national primary school students at their final year, before proceeding to five years of secondary education.
In Sweden kids go to the primary school (grundskola) through the ages of 7 and 16. After that they can choose to (although it is pretty uncommon not to) study at a gymnasium for three years where they pick a program devoted to a particlar direction (i.e. Science, Aesthetics, Civics). During the gymnasium all students have some subjects they have to study, but not during all three years. Almost all children attend a preparatory year at the age of 6. This initial year is not mandatory.
The children don't start receiving grades until their eighth year. This is, however, about to change according to a new proposal from the Swedish government, where grades will be given from the sixth year.
Nowadays, it's also possible to begin one year earlier, and the child who does will have to ability to go to and finish gymnasium one year earlier as well.
In the UK schools providing primary education in the state sector are known as primary schools. They generally cater for children aged from four to eleven (Reception to Year Six; in Scotland Primary One to Primary Seven). Primary schools are often subdivided into infant schools for children from age 4-7 (Foundation Stage and Key Stage 1) and junior schools for ages 7-11 (Key Stage 2). (Excluding Scotland, where all from age 5-12 are catered for in the one institution.)
In areas that adopted a three-tier system, the term Primary School often used as an alternative to First School, taking in ages up to 9 or 10 years old. Although for education planning puposes, the term "primary education" in these aras will still cover the age age groups as in a two-tier system.
In the private sector fee-paying schools which provide primary education are known as preparatory schools, and they often cater for children up to the age of thirteen. As their name suggests, preparatory schools are designed to prepare pupils for entrance examinations for fee-paying independent schools.
In the United States, the term primary school is used in a general way to describe a school housing the primary grades, usually meaning kindergarten (ages five to six) to fourth grade (ages 9 to 10), fifth (ages 10 to 11), or sixth grade (ages 11 to 12), though this is more commonly referred to as an elementary school. Very few schools in the US actually use the term primary school as part of their school name and such schools are generally private schools, serving very young children.
Some county school systems have begun to establish primary schools that are separate from (and often located within close proximity of) elementary schools and house only kindergarten through second grades.
In the United States, a primary school is the same thing as an elementary school. It is for young students usually kindergarten to fifth or sixth grade. In the United States elementary school is a more common term. Primary school is often used in private or independent schools. (In private or independent schools the government does not give the schools money.)
In India, "Primary Education" means the 'Nursery', the 'Kindergarten' and four years of regular schooling thereafter. Admission to Nursery classes is for children above two years so that the age is 6+ when entering Class I. Children are taught language (mother tongue and English) reading/writing skills, basic arithmetic and quite a good amount of general information about the country, people, statesmen, great people, flora & animals. However, this is true only for schools in the urban areas. Rural schools do not have Nursery or Kindergarten; they admit straight at Class I when the child is six. Further, the rural schools use the mother tongue as medium of instruction, not resorting to English in any way. Primary education is free in government schools. Moreover, rural primary schools offer free mid-day meals to children (the government pays for it) so that the drop out rate comes down. States of West Bengal, Maharashtra, Manipur, Nagaland and Kerala have done very good work in this way of spreading primary education.
In Singapore, Primary School refers to those students who are normally between the ages of 7 to 12. Primary School is classified as P1 to P6 for Primary 1 to Primary 6 respectively. At the end of P6, students sit for a national level Primary School Leaving Exam (PSLE) which is used for placement into Secondary School. Prior to Primary School, pupils attend Kindergarten School for 2 years.