Synapsida, or mammal-like reptiles, are believed to have led to the evolution of mammals. Synapsida rose to power during the Late Carboniferous (Pennsylvanian) period and continued to be the dominant land vertebrate through the Permian and Triassic periods. One of the main characteristics of all animals classified under the subclass Synapsida is the Synapsid skull, an opening behind the eye socket that allowed for the evolution of a better jaw, is found in all mammals, past and present albeit in modified forms. Prior to the development of the synapsid type skull, reptiles had a low, flat head with jaw muscles that were arranged in such a way to allow their jaws to snap together, but not to bite together in a hard pressing motion. Thus their diets and actions were very limited. With the development of the synapsid skull many other environmental niches were opened up, drastically changing the way that those in the same environment lived and evolved, such as plants which required the evolution of better defensive characteristics.
The fossils of the order Synapsida can be split into two distinct groups, the pelycosaurs and the therapsids. The best pelycosaur fossils found, so far, come from the North American lower Permian “Red Bed” sediments, mainly in New Mexico, Oklahoma, and Texas  and Nova Scotia, as well. The therapsids, however, came to inhabit every environment on every continent. 
Morphology and Evolution
The shape and morphology of the skull took a different evolutionary turn in the synapsids and their subsequent mammalian descendants. One of the biggest changes, that paved the way and forced several other changes to take place, was the development of an antorbital fenestra ("fenestra" is latin for opening or window) behind the eye socket, called the synapsid opening. As the synapsids evolved, so did the size of this opening. It is thought that the jaw muscles were attached to this opening, which in turn aided in relieving the stress that biting puts on the back of the skull, and coupled with the elongation of the back of the skull, allowed for a stronger, more precise bite. By comparison there is the anapsid skull, which has no openings, and the diapsid skull, which has two openings. Turtles and tortoises count themselves among the living descendents with the anapsid skull, and lizards, snakes, and crocodiles are among those with a diapsid skull.
The mammal-like reptiles developed the heterodont shaped dentition with sharp edged incisors for cutting, pointed canines for tearing, and cheek teeth with flat crushing surfaces for chewing. Though they still retained the typical reptilian characteristic of replacing old and worn teeth with new teeth, as the synapsids evolved they gained the ability to keep their teeth longer. Because they were able to keep their teeth longer they were capable of developing more specialized dentition and a better precision bite. This allowed for their food to be chewed down to a pulp, easier to swallow, and thus better to digest. This, in turn, allowed for the nutrients from the food to be released and used by the body much more quickly. 
With the sphenacodonts, such as the Dimetrodon, the limbs of these later pelycosaurs started to move differently than that of reptiles or earlier synapsid. Reptiles move with their limbs facing out horizontally and moving in a side-to-side motion. Starting with the sphenacodonts, synapsids moved in an up-and-down motion as seen through the evolved structure of the joints, hips, and hind limbs. The synapsids mark the beginning of the vertical locomotion, the up-and-down movement which required the limbs to flex more and with more ease and helped the synapsid to move much quicker. Reptiles also have outward facing feet whereas the synapsid, starting with the sphenacodonts, have more forward projecting feet.
Warm Bloodedness and Insulation
The ability to regulate body temperature is a distinctive characteristic in mammals, or endotherms. Ectotherms, or reptiles, lack this ability and must rely mostly on the sun in order to warm their bodies and get their energy. This is a time consuming, and even potentially dangerous, activity, which requires that the reptile be in the sun, usually in an open space, in order to get the most warmth quickly. With the development of better locomotion, insulation, and breathing control, the later therapsids were able to get their energy from other sources and reduce their dependence on the sun as an energy source. Early synapsids, such as the pelycosaurs, were believed to have been ectotherms, due to the large nature of their bodies and the sails on their backs, which has been suggested worked in the same way as solar panels, by absorbing the heat in the morning and releasing it in the afternoon and thereby allowing for temperature control.
More advanced Therapsid animals show the evolution of a diaphragm, which allowed for the development of a larger set of lungs, which in turn made the air empty quicker and more often. The quicker air empties and fills the lung cavity, the quicker the oxygen can enter the bloodstream and tissues. This has many advantages, including better muscle use and a speedier digestion, and has a ripple effect on the animals daily activities. 
Pelycosauria was the earliest and most primitive of the synapsida reptiles, and thought to have roamed the earth as early as 300 million years ago during the Pennsylvanian Period and remained the dominant land animal for about 40 million years. Many Pelycosauria fossils show that they possessed a sail on their backs, which is generally believed to have functioned as a body temperature regulator, although there are others who believe that the sails served as a sexual dimorphic feature. They are also believed to have been oviparous, meaning egg laying, a feature distinct of reptiles. Pelycosaur are the first to have, and the reason they are categorized as Synapsida, the synapsid skull with the single opening behind the eye socket that allowed for better jaw muscle evolution. It is this skull evolution coupled with a series of lucky events, such as the drought during the Kasimovian epoch which killed off many larger terrestrial tetrapods, that led to Pelycosauria becoming the dominant land animal. 
Therapsids are the more advanced of the order Synapsid, the direct ancestors of mammals. The Therapsids grew to much importance after surviving the Permian extinction and became much more widespread than their ancestors, the Pelycosauria. Even though they split off into several suborders, the only one to survive into the Jurassic Period was the cynodont suborder. Many of the therapsids have been found in places like Europe, Africa (mainly South Africa), Antarctica, Asia (China and India), and South America (mostly in Argentina). This may seem like a great feat but it helps to remember that during their reign all land masses had come together to form one massive landmass called, Gondwanaland. Since these animals were so widespread, they had much variability in their size and morphology. Some a long tails, some had short tails, some were big and thick and some were skinny and set much closer to the ground. For example, one species called the Moschops was around 16ft tall, had a massive skull, and a very thick body, it would have towered over a male human.  Some animals were carnivorous while others were herbivores, and there were even a few insectivores; the skulls and dentition of which would have changed depending on their diets. For example, the carnivores were outfitted with sharper and larger incisors and canines as well as the teeth in the back which would have been used for shredding the meat (much like modern day mammals).
The dicynodonts were the largest suborder of all the therapsids, and aside from the cynodonts, were the most advanced. The most important evolution for the dicynodonts was the development of their stronger jaws. The synapsid opening in their skuls was much bigger than their previous ancestors, allowing for their muscles to be strengthened. These animals were so widespread that they were able to adapt to many different environments and use many different niches. For example, the Cistecephalus were animals that were adapted for underground life, like our present day moles. Others like the Robertia were probably adapted for life in the forest, as seen by their tooth morphology which would have been adapted for a more leafy diet. 
The suborder Cynodonts were the only species to survive the great Permian Extinction and into the Jurassic Period. These animals are the direct and closest ancestors to mammals. The word "cynodont" means dog teeth. 
The Permian Mass Extinction
Around 248 million years ago the majority of life on this planet was completely wiped out. The Permian Mass Extinction was the single greatest catastrophe in Earth’s history, exceeding the two previous extinctions and the extinction that ended the reign of the dinosaurs in the late Cretaceous period. Figures and estimates vary among different scholars, but are generally to believe to have been about sixty to ninety five percent of all marine species and some sixty to seventy five percent of terrestrial species, including around thirty five percent of amphibians, and about sixty percent of therapsids were completely destroyed. There are several different theories as to the cause of the Permian Mass Extinction. These theories come and go like fads, there is always a theory that is more popular than the last, but at the end of the day no one knows for sure what exactly caused the mass extinction that changed life on our planet. Dr. Douglas Palmer lists out several different popular theories; including catastrophe in the form of an extraterrestrial object hitting the Earth. The impact would have created a domino effect of earthquakes, tidal waves, and large amounts of dust that would block out the sun which would devastate the Earth’s life forms. Another theory is glaciation. Glaciation is accused of creating global cooling and the lowering of sea levels across the planet. These events would have made the environments on the planet inhospitable for the majority of climate specific life forms to continue to survive. The colder the temperatures got, the more animals, and thus species, would have died. Evidence of the climate changes can be found in sediment dating to the same time period as the late Permian period. Another theory is volcanism. Evidence in sediment layers suggests that there was a major volcanic eruption somewhere in what is now Siberia. The size of the eruption, it is claimed, would have sent a vast amount of ash and sulphates into the air that would have transformed the climate of the entire planet. If the eruption was large enough, and if the adjustment in global climate had lasted long enough it could have been responsible for the extinction. 
- Palmer, Dr. Douglas. ‘’The Illustrated Encyclopedia of the Prehistoric World’’. Edison, New Jersey: Chartwell Books, Inc., 2006.
• Please note that there is some disagreement for the classifying of different species and genera in the class Synapsida. As such when it comes to the different species listed above, all information has been obtained from a single source, ‘’The Illustrated Encyclopedia of the Prehistoric World’’, to ease the confusion as much as possible. As I am not an expert in the field, and seeing as how even the experts cannot agree, I do not pretend to know which source is correct and which isn’t. Classification of species is always a confusing subject, so if there is an expert or someone close to it who would like to help clarify, I welcome the suggestions.