Short answers, pulled from the story.
A topographic map shows large-scale detail and quantitative representation of relief features, typically using contour lines that connect points of equal elevation. It differs from planimetric maps, which omit elevation, from chorographic maps, which cover large regions at smaller scales, and from thematic maps, which focus on a single topic.
The Carte géométrique de la France was the first multi-sheet topographic map series to cover an entire country, completed in 1789.
The national map-making function in the United States migrated to the newly created United States Geological Survey in 1879, consolidating responsibilities that had previously been shared between the Army Corps of Engineers and the Department of the Interior.
The International Map of the World was an initiative begun in 1913 to map all of Earth's significant land areas at a scale of 1:1,000,000, planned across roughly one thousand sheets each covering four degrees of latitude by six or more degrees of longitude. The project eventually foundered without completion, though it left behind an indexing system that remains in use.
TIGER was a United States federal government initiative developed in the 1980s that compiled interlocked databases of political borders, roadways, railroads, water features, and census enumeration areas. It was used in the 1990 decennial census and later, and because it was tax-funded and unclassified, the data entered the public domain and was freely available.
In the United States, the primary national topographic map series is organised around a strict 7.5-minute grid, and maps covering one such grid cell are commonly referred to as quads or quadrangles.