Anáhuac is the term used by the aztecs to refer to the

Anáhuac is the term used by the Aztecs to refer to the territory they dominated, e.g. the empire as a whole, including tributary peoples; and as such was among the terms proposed for the name of the new country prior to independence, as in, for example, Congress of Anáhuac, another name for the Congress of Chilpancingo.[27]
Mēxihco was the Nahuatl term for the heartland of the Aztec Empire,namely, the Valley of Mexico, and its people, the Mexica, and surrounding territories which became the future State of Mexico as a division of New Spain prior to independence; compare Latium. It is generally considered to be a toponym for the valley which became the primary ethnonym for the Aztec Triple Alliance as a result, or vice versa. It has been suggested that it is derived from Mextli orMēxihtli, a secret name for the god of war and patron of the Aztecs, Huitzilopochtli, in which case Mēxihco means "Place where Mēxihtli lives".[28]
Another hypothesis suggests that the word Mēxihco derives from the mētztli ("moon"), xictli ("navel", "center" or "son"), and the suffix -co (place), in which case it means "Place at the center of the moon" or "Place at the center of the Lake Moon", inreference to Lake Texcoco.[29] The system of interconnected lakes, of which Texcoco was at the center, had the form of a rabbit, the same image that the Aztecs saw in the moon. Tenochtitlan was located at the center (or navel) of the lake (or rabbit/moon).[29] Still another hypothesis suggests that it is derived from Mēctli, the goddess of maguey.
The name of the city-state was transliterated toSpanish as México with the phonetic value of the x in Medieval Spanish, which represented the voiceless postalveolar fricative /ʃ/. This sound, as well as the voiced postalveolar fricative /ʒ/, represented by a j, evolved into a voiceless velar fricative /x/ during the sixteenth century. This led to the use of the variant Méjico in many publications in Spanish, most notably in Spain, whereas in Mexicoand most other Spanish–speaking countries México was the preferred spelling. In recent years the Real Academia Española, which regulates the Spanish language, determined that both variants are acceptable in Spanish but that the normative recommended spelling is México.[30] The majority of publications in all Spanish-speaking countries now adhere to the new norm, even though the alternative variantis still occasionally used.[31] In English, the x in Mexico represents neither the original nor the current sound, but the consonant cluster /ks/.
The official name of the country has changed as the form of government has changed. On two occasions (1821–1823 and 1863–1867), the country was known as Imperio Mexicano (Mexican Empire). All three federal constitutions (1824, 1857 and 1917, thecurrent constitution) used the name Estados Unidos Mexicanos[32]—or the variants Estados Unidos mexicanos[33] and Estados-Unidos Mexicanos,[34] all of which have been translated as "United Mexican States". The term República Mexicana, "Mexican Republic" was used in the 1836 Constitutional Laws.[35]
History
Main article: History of Mexico

Archaeological sites of Chichén-Itzá, one of the New SevenWonders of the World
Ancient cultures
The earliest human remains in Mexico are chips of stone tools found near campfire remains in the Valley of Mexico and radiocarbon-dated to ca. 21,000 BCE.[36] Around 9,000 years ago, ancient indigenous peoples domesticated corn and initiated an agricultural revolution, leading to the formation of many complex civilizations. Between 1,800 and 300 BCE, manymatured into advanced pre-Columbian Mesoamerican civilizations such as: the Olmec, the Teotihuacan, the Maya, the Zapotec, the Mixtec, the Toltec and the Aztec, which flourished for nearly 4,000 years before the first contact with Europeans.
These civilizations are credited with many inventions and advancements in fields such as architecture (pyramid-temples), mathematics, astronomy, medicine and...