A pyramid (from Greek: πυραμίς pyramís)   is a structure whose outer surfaces are triangular and converge to a single step at the top, making the shape roughly a pyramid in the geometric sense. The base of a pyramid can be trilateral, quadrilateral, or of any polygon shape. As such, a pyramid has at least three outer triangular surfaces (at least four faces including the base). The square pyramid, with a square base and four triangular outer surfaces, is a common version.
A pyramid's design, with the majority of the weight closer to the ground  and with the pyramidion at the apex, means that less material higher up on the pyramid will be pushing down from above. This distribution of weight allowed early civilizations to create stable monumental structures.
Civilizations in many parts of the world have built pyramids. The largest pyramid by volume is the Mesoamerican Great Pyramid of Cholula, in the Mexican state of Puebla. For thousands of years, the largest structures on Earth were pyramids—first the Red Pyramid in the Dashur Necropolis and then the Great Pyramid of Khufu, both in Egypt—the latter is the only one of the Seven Wonders of the Ancient World still remaining.
The Mesopotamians built the earliest pyramidal structures, called ziggurats. In ancient times, these were brightly painted in gold/ bronze. Since they were constructed of sun-dried mud-brick, little remains of them. Ziggurats were built by the Sumerians, Babylonians, Elamites, Akkadians, and Assyrians for local religions. Each ziggurat was part of a temple complex which included other buildings. The precursors of the ziggurat were raised platforms that date from the Ubaid period  during the fourth millennium BC. The earliest ziggurats began near the end of the Early Dynastic Period.  The latest Mesopotamian ziggurats date from the 6th century BC.
Built in receding tiers upon a rectangular, oval, or square platform, the ziggurat was a pyramidal structure with a flat top. Sun-baked bricks made up the core of the ziggurat with facings of fired bricks on the outside. The facings were often glazed in different colors and may have had astrological significance. Kings sometimes had their names engraved on these glazed bricks. The number of tiers ranged from two to seven. It is assumed that they had shrines at the top, but there is no archaeological evidence for this and the only textual evidence is from Herodotus.  Access to the shrine would have been by a series of ramps on one side of the ziggurat or by a spiral ramp from base to summit.
The most famous pyramids are the Egyptian ones — huge structures built of bricks or stones, some of which are among the world's largest constructions. They are shaped as a reference to the rays of the sun. Most pyramids had a polished, highly reflective white limestone surface to give them a shining appearance when viewed from a distance. The capstone was usually made of hard stone – granite or basalt – and could be plated with gold, silver, or electrum and would also be highly reflective.  The ancient Egyptians built pyramids from 2700 BC until around 1700 BC. The first pyramid was erected during the Third Dynasty by the Pharaoh Djoser and his architect Imhotep. This step pyramid consisted of six stacked mastabas. The largest Egyptian pyramids are those at the Giza pyramid complex. 
The age of the pyramids reached its zenith at Giza in 2575–2150 BC.  Ancient Egyptian pyramids were, in most cases, placed west of the river Nile because the divine pharaoh's soul was meant to join with the sun during its descent before continuing with the sun in its eternal round.  As of 2008, some 135 pyramids have been discovered in Egypt.   The Great Pyramid of Giza is the largest in Egypt and one of the largest in the world. At 481 ft, it was the tallest building in the world until Lincoln Cathedral was finished in 1311 AD. The base is over 52,600 square metres (566,000 sq ft) in area. The Great Pyramid of Giza is one of the Seven Wonders of the Ancient World. It is the only one to survive into modern times. The Ancient Egyptians covered the faces of pyramids with polished white limestone, containing great quantities of fossilized seashells.  Many of the facing stones have fallen or have been removed and used for construction in Cairo.
Most pyramids are located near Cairo, with only one royal pyramid being located south of Cairo, at the Abydos temple complex. The pyramids at Abydos, Egypt were commissioned by Ahmose I who founded the 18th Dynasty and the New Kingdom.  The building of pyramids began in the Third Dynasty with the reign of King Djoser.  Early kings such as Snefru built several pyramids, with subsequent kings adding to the number of pyramids until the end of the Middle Kingdom.
The last king to build royal pyramids was Ahmose,  with later kings hiding their tombs in the hills, such as those in the Valley of the Kings in Luxor's West Bank.  In Medinat Habu, or Deir el-Medina, smaller pyramids were built by individuals. Smaller pyramids with steeper sides were also built by the Nubians who ruled Egypt in the Late Period. 
While pyramids are associated with Egypt, the nation of Sudan has 220 extant pyramids, the most numerous in the world.  Nubian pyramids were constructed (roughly 240 of them) at three sites in Sudan to serve as tombs for the kings and queens of Napata and Meroë. The pyramids of Kush, also known as Nubian Pyramids, have different characteristics than the pyramids of Egypt. The Nubian pyramids were constructed at a steeper angle than the Egyptian ones. Pyramids were still being built in Sudan as late as 200 AD.
The pyramidal Tomb of the Askia Muhammad I emperor of Songhai in Gao is the perfect example of the monumental mud constructions of the Sahel, it is the central element of the architectural complex extending over 4.24ha (456,000 sq ft) which constitutes the Mausoleum of the Emperor with two mosque and a Cemetery, the pyramid measures 17 meters in height with two levels upstairs. It is built of Mud and riddled with numerous wooden pikes. The architecture of the pyramid is close to the Meidum pyramid of the pharaoh Sneferu of Egypt. The pyramid-mausoleum is built by Emperor Askiya the great (1493-1528) of the Songhai Empire in the 15th century after his pilgrimage to Mecca, it serves more as a Minaret for the two mosques and the pious Muslim emperor is modestly buried in the unbuilt cemetery of the mausoleum, the intrepid conqueror Askia Muhammad I, genius administrator and man of culture is among the greatest emperors of the Songhai Empire one of the largest contiguous land empire in history and the largest and powerful in African history , it extended over the Sahel, West Africa, the Maghreb and Central Africa in the 15th and 16th centuries. The Songhai are a population belonging to the same Ethnolinguistic Nilo-Saharan group as the Nubian builders of the pyramids of Nubia, both populations are close to the ancient Egyptians. The other pyramidal constructions of the songhai country are the minaret of the Djinguereber Mosque of Timbuktu, the minaret of the Sankore university of Timbuktu and the three tower-minarets of the Mosque of Djenne. The pyramid is listed as a World Heritage Site by UNESCO. It was the target of jihadist attacks during the Mali War, but the Songhai population of Gao sees to its maintenance each year and these two mosques are still in service. It is the last Tomb - pyramid built by an African Sovereign. 
One of the unique structures of Igbo culture was the Nsude Pyramids, at the Nigerian town of Nsude, northern Igboland. Ten pyramidal structures were built of clay/mud. The first base section was 60 ft. in circumference and 3 ft. in height. The next stack was 45 ft. in circumference. Circular stacks continued, till it reached the top. The structures were temples for the god Ala, who was believed to reside at the top. A stick was placed at the top to represent the god's residence. The structures were laid in groups of five parallel to each other. Because it was built of clay/mud like the Deffufa of Nubia, time has taken its toll requiring periodic reconstruction. 
Pausanias (2nd century AD) mentions two buildings resembling pyramids, one, 19 kilometres (12 mi) southwest of the still standing structure at Hellenikon,  a common tomb for soldiers who died in a legendary struggle for the throne of Argos and another which he was told was the tomb of Argives killed in a battle around 669/8 BC. Neither of these still survive and there is no evidence that they resembled Egyptian pyramids.
There are also at least two surviving pyramid-like structures still available to study, one at Hellenikon and the other at Ligourio/Ligurio, a village near the ancient theatre Epidaurus. These buildings were not constructed in the same manner as the pyramids in Egypt. They do have inwardly sloping walls but other than those there is no obvious resemblance to Egyptian pyramids. They had large central rooms (unlike Egyptian pyramids) and the Hellenikon structure is rectangular rather than square, 12.5 by 14 metres (41 by 46 ft) which means that the sides could not have met at a point.  The stone used to build these structures was limestone quarried locally and was cut to fit, not into freestanding blocks like the Great Pyramid of Giza.[ citation needed]
The dating of these structures has been made from the pot shards excavated from the floor and on the grounds. The latest dates available from scientific dating have been estimated around the 5th and 4th centuries. Normally this technique is used for dating pottery, but here researchers have used it to try to date stone flakes from the walls of the structures. This has created some debate about whether or not these structures are actually older than Egypt, which is part of the Black Athena controversy. 
Mary Lefkowitz has criticised this research. She suggests that some of the research was done not to determine the reliability of the dating method, as was suggested, but to back up an assumption of age and to make certain points about pyramids and Greek civilization. She notes that not only are the results not very precise, but that other structures mentioned in the research are not in fact pyramids, e.g. a tomb alleged to be the tomb of Amphion and Zethus near Thebes, a structure at Stylidha (Thessaly) which is just a long wall, etc. She also notes the possibility that the stones that were dated might have been recycled from earlier constructions. She also notes that earlier research from the 1930s, confirmed in the 1980s by Fracchia was ignored. She argues that they undertook their research using a novel and previously untested methodology in order to confirm a predetermined theory about the age of these structures. 
Liritzis responded in a journal article published in 2011, stating that Lefkowitz failed to understand and misinterpreted the methodology. 
The Pyramids of Güímar refer to six rectangular pyramid-shaped, terraced structures, built from lava stone without the use of mortar. They are located in the district of Chacona, part of the town of Güímar on the island of Tenerife in the Canary Islands. The structures have been dated to the 19th century and their original function explained as a byproduct of contemporary agricultural techniques.
Autochthonous Guanche traditions as well as surviving images indicate that similar structures (also known as, "Morras", "Majanos", "Molleros", or "Paredones") could once have been found in many locations on the island. However, over time they have been dismantled and used as a cheap building material. In Güímar itself there were nine pyramids, only six of which survive.
The 27-metre-high Pyramid of Cestius was built by the end of the 1st century BC and still exists today, close to the Porta San Paolo. Another one, named Meta Romuli, standing in the Ager Vaticanus (today's Borgo), was destroyed at the end of the 15th century. 
A number of Mesoamerican cultures also built pyramid-shaped structures. Mesoamerican pyramids were usually stepped, with temples on top, more similar to the Mesopotamian ziggurat than the Egyptian pyramid.
The largest pyramid by volume is the Great Pyramid of Cholula, in the Mexican state of Puebla. Constructed from the 3rd century BC to the 9th century AD, this pyramid is considered the largest monument ever constructed anywhere in the world, and is still being excavated. The third largest pyramid in the world, the Pyramid of the Sun, at Teotihuacan is also located in Mexico. There is an unusual pyramid with a circular plan at the site of Cuicuilco, now inside Mexico City and mostly covered with lava from an eruption of the Xitle Volcano in the 1st century BC. There are several circular stepped pyramids called Guachimontones in Teuchitlán, Jalisco as well.
Pyramids in Mexico were often used as places of human sacrifice. For the re-consecration of Great Pyramid of Tenochtitlan in 1487, Where, according to Michael Harner, "one source states 20,000, another 72,344, and several give 80,400". 
Many pre-Columbian Native American societies of ancient North America built large pyramidal earth structures known as platform mounds. Among the largest and best-known of these structures is Monks Mound at the site of Cahokia in what became Illinois, completed around 1100 AD, which has a base larger than that of the Great Pyramid at Giza. Many of the mounds underwent repeated episodes of mound construction at periodic intervals, some becoming quite large. They are believed to have played a central role in the mound-building peoples' religious life and documented uses include semi-public chief's house platforms, public temple platforms, mortuary platforms, charnel house platforms, earth lodge/town house platforms, residence platforms, square ground and rotunda platforms, and dance platforms.    Cultures who built substructure mounds include the Troyville culture, Coles Creek culture, Plaquemine culture and Mississippian cultures.
There are many square flat-topped mound tombs in China. The First Emperor Qin Shi Huang (circa 221 BC, who unified the 7 pre-Imperial Kingdoms) was buried under a large mound outside modern day Xi'an. In the following centuries about a dozen more Han Dynasty royals were also buried under flat-topped pyramidal earthworks.
Numerous giant, granite, temple pyramids were made in South India during the Chola Empire, many of which are still in religious use today. Examples of such pyramid temples include Brihadisvara Temple at Thanjavur, the Brihadisvara Temple at Gangaikonda Cholapuram, and the Airavatesvara Temple at Darasuram. However, the temple pyramid that has the largest area is the Ranganathaswamy Temple in Srirangam, Tamil Nadu. The Thanjavur temple was built by Raja Raja Chola in the 11th century. The Brihadisvara Temple was declared a World Heritage Site by UNESCO in 1987; the Temple of Gangaikondacholapuram and the Airavatesvara Temple at Darasuram were added as extensions to the site in 2004. 
Next to menhir, stone table, and stone statue; Austronesian megalithic culture in Indonesia also featured earth and stone step pyramid structures called punden berundak as discovered in Pangguyangan site near Cisolok  and in Cipari near Kuningan.  The construction of stone pyramids is based on the native beliefs that mountains and high places are the abode for the spirit of the ancestors. 
The step pyramid is the basic design of 8th century Borobudur Buddhist monument in Central Java.  However the later temples built in Java were influenced by Indian Hindu architecture, as displayed by the towering spires of Prambanan temple. In the 15th century Java during late Majapahit period saw the revival of Austronesian indigenous elements as displayed by Sukuh temple that somewhat resemble Mesoamerican pyramid, and also stepped pyramids of Mount Penanggungan. 
In east Asia, Buddhist stupas had been usually represented as tall Pagodas. However, some pyramidal stupas remain in limited areas. There is a theory that these pyramid were inspired by Borobudur monument through Sumatran and Javanese monks.  Also, there is similar Buddhist monument in Vrang, Tajikistan.   At least there are at least 9 Buddhist step pyramids in the world, 4 from former Gyeongsang Province of Korea, 3 from Japan, 1 from Indonesia (Borobudur) and 1 from Tajikistan.  
With the Egyptian Revival movement in the nineteenth and early twentieth century, pyramids were becoming more common in funerary architecture. This style was especially popular with tycoons in the US. Hunt's Tomb in Phoenix, Arizona and Schoenhofen Pyramid Mausoleum in Chicago are some of the notable examples. Even today some people build pyramid tombs for themselves. Nicolas Cage bought a pyramid tomb for himself in a famed New Orleans graveyard. 
Stockport Pyramid in Stockport, United Kingdom
Karlsruhe Pyramid, Germany
Metairie Cemetery, New Orleans
Zafer Plaza shopping center in Bursa, Turkey
"Pyramid" culture-entertainment complex in Kazan, Russia.