Short answers, pulled from the story.
A foundation connects a structure to the ground, transferring its loads safely into the soil or rock below. It distributes the building's weight to prevent unequal settlement, anchors the structure against forces such as earthquakes, floods, and wind, and provides a stable, level base for construction.
Shallow foundations, often called footings, are embedded roughly a meter into the soil and transfer loads near the surface; common types include spread footings and slab-on-grade slabs. Deep foundations, such as driven piles, drilled shafts, and caissons, pass through weak upper topsoil to reach stronger subsoil layers below.
A rubble-trench foundation is a shallow trench filled with rubble or stones that extends below the frost line, sometimes fitted with a drain pipe to remove groundwater. It is suitable for soils with a bearing capacity of more than 10 tonnes per square meter (2,000 pounds per square foot).
A monopile foundation is a single large-diameter structural element driven into the earth to support all the loads of a large above-surface structure. It is widely used for fixed-bottom offshore wind farms; a wind farm off the coast of England that came online in 2008 used monopiles 4.74 meters in diameter in ocean depths of up to 16 meters.
Differential settlement occurs when one part of a foundation sinks more than another, typically because superimposed loads are not uniformly distributed or because the underlying soil varies in strength. Expansive clay soils, which swell when wet and shrink when dry, are a common contributing factor.
A padstone is a single stone placed beneath a timber structure to spread its load over a small area and raise the wood off damp ground; staddle stones are a specific variety. Unlike post-in-ground construction, which embeds timber directly in soil with no true foundation, a padstone provides a distinct load-distributing element between the structure and the earth.