Mexico is the usual name in the world for the country officially called the United Mexican States, it is a federal republic made up of 31 states and a Federal District  that according to the current Constitution is the seat of the powers of the federation, also the federal capital is known as Mexico City.
It limits the north with the United States of America ; to the east, with the Gulf of Mexico and the Caribbean Sea ; to the southeast, with Belize and Guatemala, and to the west with the Pacific Ocean. The Mexican area occupies an area of close to 2 million km², which places it in the fourteenth position among the list of countries ordered by area. Its population is over 112 million people (2010 data), making it the most populous Spanish-speaking nation in the world. On the other hand, the Spanish language coexists in Mexico with numerous indigenous languages.
Olmec civilization, Mesoamerican culture considered the mother of the later cultures of the Mayans and Aztecs.
The territory of Mesoamerica  includes the center and south of the current Mexican territory and Central America. In this area, with a great variety of natural wealth and habitat types (tropical forests, high mountains, deserts, mangroves, valleys, savannas, etc.), pre-Hispanic Mexican civilizations settled. The specialists and scholars of the ancient history of Mexico divide this territory into different regions in which a particular culture predominated  :
- Central Highlands: Tolteca, Mexica, Teotihuacana
- Mayan Area: Mayas
- Gulf of Mexico: Olmeca, Totonaca
- West: Purépechas
- Oaxaca Valley: Zapotec and Mixteca
Despite the little information about the period in which these civilizations inhabited, historians have established three major periods that are detailed in the following table: 
|Preclassic||2500 BC – 200||Olmec, Zapotec and Mayan|
|Classic||200 – 900||Zapotecs, Teotihuacanos and Maya|
|Postclassic||900 – 1521||Mayans, Toltecs, Mixtecs, Purépachas and Mexica|
During the beginning of the Early Preclassic or Preclassic  the displayed ceramic, new crops of corn and sedentary lifestyles. In the intermediate pre-classic period, the construction of large complexes began, such as religious temples. Small villages become centers of important politics and religion. With the passage of time they become large cities.
In the year 800 BC emerges in the Gulf of Mexico the people Olmeca, the most important culture of this period. Other peoples of this era, the Zapotecs, innovate in the methods used for agriculture and construction in general, with the use of stones, which represented an important evolution in these branches. They developed a writing system and showed deep astronomical knowledge. (The first calendars were found that are believed to be the basis of the famous Mayan calendars).
In the late pre-classic period  an important ceremonial center arises in Monte Albán that had a great Olmec influence. Some small ceremonial centers also appear in the Maya lowlands. The pyramid of Cuicuilco is built and Teotihuacan begins to be erected.
The classical period  is between the years 200 to 900 of our era. It is characterized by the evolution of the social and political institutions developed in the previous period. the religion it continues to be the center of power of the dominant cities, in a society that is known to be highly stratified. The lord of a city was a man-god who embodied in his person one of these divinities. These residents deeply obedient to gods more powerful and important than the previous period owed the same servility to their representative on earth: the high priest to whom we referred. This is a stage marked by sacrifices and offerings of all kinds. Commercial relations are established between the most important cities such as Tlaxcala, Coliman, Oaxaca, Teotihacan, Mexico and Puebla.
It is necessary to emphasize the role of Teotihuacan as a religious and commercial center of Mesoamerica and the world. Together with China, India, Peru and Egypt they represent the first complex states in human history. By the year 400 of our era, it is believed that it had around 200,000 residents, who gave the city a splendor that it would enjoy for 300 years, suddenly disappearing due to causes that still have no exact explanations today.
The post-classical period  is between the years 800 until the Spanish conquest (1521). In this stage, several peoples called Chichimecas, residents of the area beyond the northern limit of Mesoamerica, advance south in search of the resources of which, for different reasons, they were deprived. The 300-year-long process caused structural changes in the political and social geography of the territories. Tula, center of one of the Chichimeca peoples: the Toltecs, imposed the veneration for Quetzalcoatl, which will have great significance at the time of the Spanish conquest. Around 1320 the Mexica (the first people in history to introduce compulsory and egalitarian education) carry out the construction, upon seeing a snake being eaten by an eagle, of one of the most spectacular cities in known history: Tenochtitlan, whose hegemony will soon be imposed over the central area of these territories and that will extend to the south.
Thanks to ingenious constructions on the surrounding lakes, they turn this city into a militarily impregnable bastion. Its economy was based on agriculture and the tributes of the subject peoples. The Aztec empire was ruled by Moctezuma Ilhuicamina, succeeded by Axayacatl, Tizoc and Ahuizotl. The subjugation of neighboring towns was also justified by the human sacrifices they carried out, for which they needed prisoners. Seventy buildings surrounded the Templo Mayor, many of them reserved for government and worship, and some with a pyramidal shape; great streets and aqueducts. Tenochtitlan was an empire that seemed to have no rivals. Its last ruler, Moctezuma II was a true tyrant, who succumbed together with his gods to the new ones after the Spanish conquest.
The conquest of Mexico by the Spanish began in 1517   when Diego Velázquez, governor of the island of Cuba, authorized the explorer Francisco Hernández de Córdoba to carry out an expedition to find lands south of the island of Cuba; Hernández de Córdoba makes landfall at Cape Catoche in the current Yucatan peninsula after skirting the coast, he also does so in Campotón in the current state of Campeche, upon his return to Cuba where he dies as a result of injuries caused in an indigenous attack. that he saw and discovered in the new lands. The following year, Diego Velázquez He sent 4 boats under the command of Juan de Grijalva, who arrived in Tabasco and sailed the river that today bears his name. The expedition of 1519  , led by Hernán Cortés, made landfall first in Cozumel and reached the coast of Tabasco, where the Battle of Centla was fought against the Mayans of Potonchán.
Cortés later founded Santa María de la Victoria  , the first Spanish town in Mexico. At that point, the indigenous people presented Malintzin, whose role as an interpreter was of great help in the conquest of the Mesoamericans. From there, the Spaniards embarked for Villa Rica de la Vera Cruz, the second Spanish town founded in Mexican territory on July 10, 1519  .
The Spanish managed to establish alliances with various indigenous peoples, including the Totonacs and the Tlaxcalans. Together they advanced towards central Mexico and on the way defeated some allies of the Mexica, such as Cholula. Moctezuma Xocoyotzin received the newcomers peacefully. I thought it was the fulfillment of an ancient prophecy. After the Tóxcatl massacre, the Mexica rose up against the Spanish and their allies. Cuitláhuac invaders defeated the 30 of June of 1520, and died shortly afterwards during the epidemic of huey cocoliztli. Cuauhtémoc, abandoned by most of his allies, was captured on August 13, 1521  , and executed by the Spanish in 1525. Capturing the city of Mexico-Tenochtitlán, the Spanish proceeded to the subjugation of other peoples. Some voluntarily submitted, and others put up military resistance. Some indigenous peoples did not submit until the 19th century.
With the Spanish military, missionaries also arrived who played an important role in the conquest while evangelizing the indigenous people. Of the religious who arrived in the country, Vasco de Quiroga, Motolinía, Martín de Valencia, Bernardino de Sahagún, Diego de Landa, Junípero Serra, Sebastián de Aparicio and Bartolomé de las Casas stood out.
Viceroyalty of New Spain (1521-1810)
Once Tenochtitlan was subdued, Hernán Cortés assumed the government as captain general of New Spain. In 1527 the Audiencia de México was established. The first viceroy was Antonio de Mendoza and he ruled from 1535  . New Spain was ruled by 63 viceroys during the nearly 300 years of Spanish rule.
Throughout the viceregal period, the power of the Spanish was consolidated through the subjugation of the indigenous peoples. The Mixtón War (1540 – 1551) and the Chichimeca War (1546) manifest the conflicts that the Spanish faced when expanding their dominions towards the north of New Spain. The process of expansion to the north continued until the independence of Mexico. In the Californias and New Mexico, this process was reinforced by the mission system to Christianize the Indians, which caused episodes of violence such as the Rebellion of the Pericúes (1734 – 1737).
Mining allowed the development of other associated activities, especially obrajes and agriculture, which turned the regions of the Bajío and the valleys of Mexico and Puebla into agricultural regions and incipient industrial activity  .
The trade of the viceroyalty was carried out through two ports: Veracruz (Gulf of Mexico) and Acapulco (Pacific Ocean)  . The Nao de China arrived at the latter, which transported products from the Philippines to New Spain and from there they were transported by land, arriving in Puebla, where the oriental influence is notorious in its crafts and in its traditions such as that of the “china poblana”, to the City Hall of Mexico and to Veracruz from where it was sent to Spain or the Atlantic ports. Trade contributed to the flourishing of these ports, of Mexico City and the intermediate regions. It should be noted that until the end of the 18th century With the introduction of the Bourbon reforms, trade between the Spanish viceroyalties was not allowed.
The viceroyalty was the base of the cultural and racial mosaic of present-day Mexico. In its bosom, indigenous and European cultures merged over 300 years. Likewise, there was a lot of racial mixing. Figures such as Sor Juana Inés de la Cruz and Juan Ruiz de Alarcón stand out as their most notable contributors to New Hispanic literature, as well as Manuel Tolsá in architecture. Regarding financial institutions, Pedro Romero de Terreros, founder of the Sacro y Real Monte de Piedad de Ánimas, the antecedent of the National Monte de Piedad (also called Monte Pío), the genesis of microcredit worldwide, stood out. Also noteworthy are the chemical discoveries of Andrés Manuel del Río, discoverer of Erythronium, later renamed Vanadium, in the periodic table of chemical elements.
Most of the New Hispanic society professed the Catholic religion  . The Holy Inquisition —which sought to suppress indigenous idolatries— had its offices installed in the territory. The territory of New Spain was large enough for a large number of indigenous peoples and a great variety of languages to exist in it, not excluding Europeans. During the three hundred years of New Spain, there were different legal provisions that affected the commerce and prosperity of New Spain. In general, their level of prosperity was the highest in America, especially the residents of the municipalities of Mexico, Puebla de los Angeles, Villa Rica de la Veracruz, Acapulco and Zacatecas. Although an integration policy was proposed as a general rule, the political reality that imposed the granting of important positions for the Spanish bureaucracy (especially since the arrival of the Bourbons, who advocated the French model of colonization, against which Creoles or children of Spaniards born in Mexico began to rebel). In addition, divisions as serious as the castes were created in Yucatán.