Mam is one of the three Ancient Dialects that Lara can learn in Shadow of the Tomb Raider. The other two are Quechua and Yucatec. Like these, Mam is a real language that is still spoken today by the Maya people of Meso-America. During the course of the game Lara is able to improve her Language Proficiency in all of these languages by finding relics and murals. Many of the inhabitants of Paititi use one of these languages when the game is set to use the Immersion Mode.
Mam is actually the first language Lara starts learning during the game. The first Mural she comes across - called Heart of the Serpent - during the story mode is located in Cozumel region in Mexico and can be found in the Hunters Moon level.
In Real Life
Mam is spoken by 500.000 to 600.000 people - also called Mam - in Guatemala and southern Mexico. There are multiple dialects that differ wildly from village to village, and speakers of different dialect may have problems understanding each other. While during the Spanish rule it was forbidden to write down any indigenous language, Mam nowadays is protected by law in the countries it is spoken in.