Franz Anton Mesmer (born Friedrich Anton Mesmer; May 23, 1734 – March 5, 1815) was a German physician and astrologist, who discovered what he called magnétisme animal (animal magnetism) and other spiritual forces often grouped together as mesmerism. The evolution of Mesmer's ideas and practices led Scottish surgeon James Braid to develop hypnosis in 1842. Mesmer's name is the root of the English verb "mesmerize".

Mesmer was born in the village of Izang, on the shore of Lake Constance in Swabia, Germany. After studying at the Jesuit universities of Dillingen and Ingolstadt, he took up the study of medicine at the University of Vienna in 1759. In 1766 he published a doctoral dissertation with the Latin title De planetarum influxu in corpus humanum (On the Influence of the Planets on the Human Body), which discussed the influence of the Moon and the planets on the human body and on disease. This was not medical astrology—relying largely on Newton's theory of the tides, Mesmer expounded on certain tides in the human body that might be accounted for by the movements of the sun and moon.. Evidence assembled by Frank A. Pattie suggests that Mesmer plagiarized his dissertation from a work by Richard Mead, an eminent English physician and Newton's friend. That said, in Mesmer's day doctoral theses were not expected to be original.

In January 1768, Mesmer married a wealthy widow and established himself as a physician in the Austrian capital Vienna. He lived on a splendid estate and became a patron of the arts. In 1768, when court intrigue prevented the performance of La Finta Semplice (K. 51) for which a twelve-year-old Wolfgang Amadeus Mozart had composed 500 pages of music, Mesmer is said to have arranged a performance in his garden of Mozart's Bastien und Bastienne (K. 50), a one-act opera, though Mozart's biographer Nissen has stated that there is no proof that this performance actually took place. Mozart later immortalized his former patron by including a comedic reference to Mesmer in his opera Così fan tutte.