Dimetrodon (/daɪˈmiːtrəˌdɒn/ or /daɪˈmɛtrəˌdɒn/ ^ⓘ; lit. 'two measures of teeth') is an extinct genus of sphenacodontid synapsid that lived during the Cisuralian to early Guadalupian epoch of the Permian period, around 294.1–271 million years ago. With most species measuring 1.7–4.6 m (5.6–15.1 ft) long and weighing 28–250 kg (62–551 lb), the most prominent feature of Dimetrodon is the large neural spine sail on its back formed by elongated spines extending from the vertebrae. It was an obligate quadruped (it could walk only on four legs) and had a tall, curved skull with large teeth of different sizes set along the jaws. Most fossils have been found in the Southwestern United States, the majority of these coming from a geological deposit called the Red Beds of Texas and Oklahoma. More recently, its fossils have also been found in Germany and over a dozen species have been named since the genus was first erected in 1878.

Dimetrodon is often mistaken for a dinosaur or portrayed as a contemporary of dinosaurs in popular culture, but it became extinct by the middle Permian, some 40 million years before the appearance of dinosaurs. Although reptile-like in appearance and physiology, Dimetrodon is much more closely related to mammals, as it belongs to the closest sister family to therapsids, the latter of which contains the direct ancestor of mammals. Dimetrodon is traditionally assigned to the paraphyletic group "pelycosaurs", a term now considered obsolete and replaced by terms such as "primitive synapsids" or "basal synapsids"; the name "mammal-like reptiles" is also traditionally used for non-mammalian synapsids due to some of the features shared with modern mammals such as tooth specialization and endothermy, but that term is now also defunct. The Dimetrodon skull has a single opening (temporal fenestra) behind each eye, a feature shared among all synapsids, unlike the skulls of reptiles and birds, both of which belong to the clade Sauropsida, which had diverged from the synapsids by the Late Carboniferous.

Dimetrodon was probably one of the apex predators of the Cisuralian ecosystems, feeding on fish and tetrapods, including reptiles and amphibians. Smaller Dimetrodon species may have had different ecological roles. The sail of Dimetrodon may have been used to stabilize its spine or to heat and cool its body as a form of thermoregulation. Some recent studies argue that the sail would have been ineffective at removing heat from the body, due to large species being discovered with small sails and small species being discovered with large sails, essentially ruling out heat regulation as its main purpose. The sail was most likely used in courtship display, including threatening away rivals or showing off to potential mates.

The earliest discovery of Dimetrodon fossils were of a maxilla recovered in 1845 by a man named Donald McLeod, living in the British colony of Prince Edward Island (modern Canada). These fossils were purchased by John William Johnson, a Canadian geologist, and then described by Joseph Leidy in 1854 as the mandible of Bathygnathus borealis, a large carnivore related to Thecodontosaurus, although it was later reclassified as a species of Dimetrodon in 2015, as Dimetrodon borealis. Although Bathygnathus was named first, a petition to conserve the genus Dimetrodon and suppress the genus Bathygnathus was submitted to the International Commission on Zoological Nomenclature (ICZN) in 2015, which was approved in 2019.

Fossils now attributed to Dimetrodon were first studied by American paleontologist Edward Drinker Cope in the 1870s. Cope had obtained the fossils along with those of many other Permian tetrapods from several collectors who had been exploring a group of rocks in Texas called the Red Beds. Among these collectors were Swiss naturalist Jacob Boll, Texas geologist W. F. Cummins, and amateur paleontologist Charles Hazelius Sternberg. Most of Cope's specimens went to the American Museum of Natural History or to the University of Chicago's Walker Museum (most of the Walker fossil collection is now housed in the Field Museum of Natural History).

Sternberg sent some of his own specimens to German paleontologist Ferdinand Broili at the Ludwig-Maximilians-Universität München, although Broili was not as prolific as Cope in describing specimens. Cope's rival Othniel Charles Marsh also collected some bones of Dimetrodon, which he sent to the Walker Museum. The first use of the name Dimetrodon came in 1878 when Cope named the species Dimetrodon incisivus, Dimetrodon rectiformis, and Dimetrodon gigas in the scientific journal Proceedings of the American Philosophical Society.

The first description of a Dimetrodon fossil came a year earlier, though, when Cope named the species Clepsydrops limbatus from the Texas Red Beds. (The name Clepsydrops was first coined by Cope in 1875 for sphenacodontid remains from Vermilion County, Illinois, and was later employed for many sphenacontid specimens from Texas; many new species of sphenacodontids from Texas were assigned to either Clepsydrops or Dimetrodon in the late 19th and early 20th centuries.) C. limbatus was reclassified as a species of Dimetrodon in 1940, meaning that Cope's 1877 paper was the first record of Dimetrodon.

Cope was the first to describe a sail-backed synapsid with the naming of C. natalis in his 1878 paper, although he called the sail a fin and compared it to the crests of the modern basilisk lizard (Basilicus). Sails were not preserved in the specimens of D. incisive and D. gigas that Cope described in his 1878 paper, but elongated spines were present in the D. rectiformis specimen he described. Cope commented on the purpose of the sail in 1886, writing, "The utility is difficult to imagine. Unless the animal had aquatic habits and swam on its back, the crest or fin must have been in the way of active movements... The limbs are not long enough nor the claws acute enough to demonstrate arboreal habits, as in the existing genus Basilicus, where a similar crest exists."