Treaty of Córdoba
The Treaty of Córdoba established Mexican independence from Spain at the conclusion of the Mexican War of Independence. It was signed on August 24, 1821 in Córdoba, Veracruz, Mexico. The signatories were the head of the Army of the Three Guarantees, Agustín de Iturbide, and, acting on behalf of the Spanish government, "Jefe Político Superior" Juan O'Donojú. The treaty has 17 articles, which developed the proposals of the Plan of Iguala. The Treaty is the first document in which Spanish (without authorization) and Mexican officials accept the liberty of what will become the First Mexican Empire, but it is not today recognized as the foundational moment, since these ideas are often attributed to the Grito de Dolores (September 16, 1810). The treaty was rejected by the Spanish government. Spain did not recognize Mexico's independence until December 1836.
Mexico–United States border
In the mid-16th century, after the discovery of silver, settlers from various countries and backgrounds began to arrive in the area. This period of sparse settlement included colonizers from different backgrounds. The area was part of New Spain, but due to the lack of population and the diverse citizenry it had, it did not seem to belong to any country. This period lasted until the early 19th century, at which point the United States bought the lands known as the Louisiana Purchase from France and began to expand steadily (militarily) westward in its pursuit of Manifest Destiny.
The border itself was not clearly defined and remained so until the Mexican colony became independent from Spain and entered a period of political instability. Mexico attempted to create a buffer zone at the border that would prevent possible invasion from the North. The Mexican government encouraged thousands of their own citizens to settle in the region that is now known as Texas and even offered inexpensive land to settlers from the United States in exchange for populating the area. The influx of people did not provide the defense that Mexico had hoped for and instead Texas declared its independence in 1836, which lasted until 1845 when the U.S. annexed it.