1 basis, base, substructure, understructure, underpinning, bottom, foot, basement, cellar:
This foundation is of stone.
2 basis, base, fundamental, (underlying or fundamental) principle, grounds, groundwork, rationale, raison d'être, purpose:
Their morality finds its foundations in Judaeo-Christian culture.
3 founding, establishment, instituting, institution, creation, origination, setting up, organizing, organization, inauguration, endowment:
We voted for the foundation of an institute to study the English language.