A normal school is a institution for training teachers. According to the Oxford English Dictionary normal schools in the United States and Canada trained primary school teachers, while in Europe, normal schools educated primary, secondary and tertiary-level teachers. Many famous universities (including the University of California, Los Angeles) originated as normal schools.

The first normal schools in the United States were founded in Massachusetts beginning in the late 1830s, thanks largely to the efforts of education reformers like Horace Mann. The first, Framingham State College, (also known as FSC), opened in 1839, in Framingham, Massachusetts. Influenced by similar such academies in Prussia and elsewhere in Europe, they were intended to improve the quality of the burgeoning common school system by producing more qualified teachers. The first normal school to open west of the Mississippi River in the United States was the institution presently known as Sam Houston State University.

The term is now archaic, and in the United States the function of normal schools has been taken up by undergraduate and graduate Schools of Education. In Canada, such institutes are usually parts of universities as the Faculty of Education offering a one-year Bachelor of Education program. It requires at least three (usually four) years of prior undergraduate studies.

The term originated in the early nineteenth century from the French école normale, because the first such schools were established as standard models to be emulated by other schools.

The terminology is preserved in the official translations of such schools in both the Republic of China and the People's Republic of China since the early 20th century. A Chinese normal university (師範大學 shifan daxue, abbreviated 師大 shida) is usually controlled by the national or provincial government. A teachers college (師範學院 shifan xueyuan, abbreviation 師院 shiyuan) has lower entrance requirements.