Foundation engineering is critical for ensuring the stability and load$-$bearing capacity of structures by transferring loads to the underlying soil or rock strata. Develop a theoretical framework elucidating the principles of foundation engineering, including soil$-$structure interaction, bearing capacity, and settlement analysis. Discuss theoretical models for predicting foundation performance under static and dynamic loading conditions, such as Terzaghi's bearing capacity theory and consolidation theory. Explore theoretical approaches to foundation design, including shallow and deep foundation systems, and analyze their suitability for various soil types and site conditions.