Prof. Karan S. Chauhan discusses different types of shallow foundations that can be used for building construction, including spread footings, combined footings, strap footings, and raft/mat foundations. Some key considerations for foundations are distributing structural loads across a large area, providing stability, and minimizing settlement. In expansive black cotton soil, deeper foundations of 1.5 meters or removal and replacement of the soil are recommended to prevent cracking from swelling and shrinkage. Specific foundation options for black cotton soil include strip footings, pier foundations, and under-reamed pile foundations.