Emigration is the act of leaving one's country or region to settle in another. It is the same as immigration but from the perspective of the country of origin. Human movement in general is termed migration. There are many reasons why people might choose to emigrate. Some are for reasons of religious, political or economic freedom or escape. Others have personal reasons such as marriage. Some people living in rich nations with cold climates choose to move to warmer climates when they retire.

Emigration had a profound influence on the world in the 18th, 19th, and 20th centuries, when millions of poor families left Europe for the United States, Canada, Brazil, Argentina, the rest of Latin America, Australia and New Zealand.

Even though definitions may be vague and vary somewhat, emigration/immigration should not be confused with the phenomenon of involuntary migration, such as instances of population transfer or ethnic cleansing.

Motives to migrate can be either incentives attracting people away, known as pull factors, or circumstances encouraging a person to leave, known as push factors, for example:

Brook Taylor FRS (18 August 1685 – 29 December 1731) was an English mathematician who is best known for Taylor's theorem and the Taylor series.

Brook Taylor was born in Edmonton (at that time in Middlesex) to John Taylor of Bifrons House, Kent, and Olivia Tempest, daughter of Sir Nicholas Tempest, Bart., of Durham.^{[citation needed]} Brook entered St John's College, Cambridge as a fellow-commoner in 1701, and took degrees of LL.B. and LL.D. in 1709 and 1714, respectively. Having studied mathematics under John Machin and John Keill, in 1708 he obtained a remarkable solution of the problem of the "centre of oscillation," which, however, remained unpublished until May 1714, when his claim to priority was disputed by Johann Bernoulli. Taylor's Methodus Incrementorum Directa et Inversa (1715) added a new branch to the higher mathematics, now designated the "calculus of finite differences." This work is available in translation on the web [1]. Among other ingenious applications, he used it to determine the form of movement of a vibrating string, by him first successfully reduced to mechanical principles. The same work contained the celebrated formula known as Taylor's theorem, the importance of which remained unrecognised until 1772, when J. L. Lagrange realized its powers and termed it "le principal fondement du calcul différentiel" ("the main foundation of differential calculus").