Founded by governor Martín de Alarcón.
Entrusted to friar Antonio de San Buenaventura y Olivares in April/May, 1718.

Mission Alamo Official Visitor Web Page. Provides a great 3D virtual visit to the Church.
San Antonio Conservation Society has Historical information about the Alamo Mission.

The address: 300 Alamo Plaza, San Antonio, TX 78205

The Mission became famous through the battle of the Alamo (1836), events which became a staff of legends and the Mission was elevated to be a national patriotic monument. Historians often confront this legend with a sober depiction of events, as found in documents, but that's another matter.

In 2017/2018 visitors had to make a reservation, were admitted by the rangers in groups and were asked to "lower their voices" while being inside, to honor the fallen of the siege. On the premises of the mission are the old barracks hosting a small museum and there is an open air exhibit. When I was in Alamo, photography in the church proper was not permitted. But I see now online numerous images of the interior. So maybe the restrictions were lifted later on?

The Church is empty, no altar, no artwork, no interior of any kind. A series of elaborate plaques commemorate the events of the 1836 battle of Alamo. The history of the Mission is well described e.g. in the Wikipedia article. During the Texas revolution the Mission changed hands several times. The site was vandalized many times by both sides. When General Juan Andrade was leaving Texas after the 1836 Battle of San Jacinto, he tore down many of the Alamo walls, and set fires throughout the complex.

On the opposite side of the city in the Cathedral San Fernando is a coffin with the exhumed remains of the most famous defenders of the Alamo. Several Hollywood movies were made about these events over the time, most famously in "The Alamo" with John Wayne (1960). The Briscoe Museum of Art at the River Walk has a great artist rendition diorama of the battle. The sword of General Santa Anna is on display in this museum.
Mission San Antonio (The Alamo) Wikipedia page.