It wasn't a country but a region dominated by several city-states. Some of them include Mexico-Tenochtitlan (ruled by the Aztec or Mexica civilization), Tlaxcala, Texcoco or the Mayan cities to the south.
Several civilizations qualify as such; from the Olmecs who first appeared in 3000 BC and are considered the progenitors to all Mesoamerican civilizations, to the Aztecs, who founded their capital city on 1325 and together with the Mayans, were eventually conquered by Spanish forces during the 16th century.
The Aztecs, up to 1521 at the Fall of Tenochtitlan.
Both Aztecs and Mayans qualify as such (they were present in Mexico when contact with Europeans was established in 1519).
Just before contact with Europeans was made in 1519, central Mexico was being ruled by the Aztec Empire.
Aztecs and Mayans were the most important; however there were many minor tribes and ethnic groups living in Mexico prior to the Spanish conquest of Mexico.
The Mayan civilization.
The Aztecs
Mexico-Tenochtitlan
The Spanish Empire controlled Mexico for over three centuries.
If you were to visit Mexico tomorrow, the best way that you would know that it was once controlled by the Spanish is the prevalence of the Spanish language.
When Spanish conquistadors arrived to Mexico, they also brought Roman Catholic priests with them. Once they conquered all native peoples in Mexico, they swiftly converted them to Christianity.
When the Spanish explorers arrived in Mexico they had priests with them. The priests convert the people they found.
Spanish conquistadors.
The Spanish
The Spanish Empire controlled much of present-day Mexico and Central America from 1521 until 1821.
Moctezuma lived in Mexico and was the ruler of Tenochtitlan until the Spanish arrived :)
The Aztecs.
The Aztec's were the last Indian empire in Mexico. They fell to the Spanish invasion in 1521. This was the beginning of 300 years of colonial rule in Mexico.
It was the Aztec civilization.