A normal school or normal college is an institution created to train teachers by educating them in the norms of pedagogy and curriculum. In the 19th century in the United States, instruction in normal schools was at the high school level, turning out primary school teachers. Many such schools are now called teacher training colleges or teachers' colleges, but in Mexico continue to be called normal schools, with student-teachers being known as normalistas. Many schools currently require a high school diploma for entry, and may be part of a comprehensive university. Normal schools in the United States, Canada and Argentina trained teachers for primary schools, while in Europe, the equivalent colleges typically educated teachers for primary schools and later extended their curricula to also cover secondary schools.

In 1685, St. Jean-Baptiste de La Salle, established the Institute of the Brothers of the Christian Schools, founded what is generally considered the first normal school, the École Normale, in Reims, Champagne, France. The term "normal" in this context refers to the goal of these institutions to instill and reinforce particular norms within students. "Norms" included historical behavioral norms of the time, as well as norms that reinforced targeted societal values, ideologies and dominant narratives in the form of curriculum.

The first public normal school in the United States was founded in Concord, Vermont by Samuel Read Hall in 1823 to train teachers. In 1839, the first state-supported normal school was established by the Commonwealth of Massachusetts on the northeast corner of the historic Lexington Battle Green; it evolved into Framingham State University. The first modern teacher training school in China was established by educator Sheng Xuanhuai in 1895 as the normal school of the Nanyang Public School (now Shanghai Jiao Tong University) in Shanghai during the Qing dynasty.

Many comprehensive public or state-supported universities—such as the UCLA in the United States and Beijing Normal University in China—were established and operated as normal schools before they expanded their faculties and transformed themselves into research universities. Some of these universities, particularly in Asia, retain the word "Normal" in their name to highlight their historical purpose. In Canada, most normal schools were eventually assimilated into a university as its faculty of education, offering a one or two-year Bachelor of Education degree. Such a degree requires at least three, but usually four, years of prior undergraduate study.