Among the titles in Official Papers on the Ground Floor are:
“Commission shall have for its object the promotion of the progressive development of international law and its codification”. (Art.1(1) Statute of ILC)
International here encompasses both public and private international law.
Article 15 of the Statute “for convenience” says progressive development means “the preparation of draft conventions on subjects which have not yet been regulated by international law or in regard to which the law has not yet been sufficiently developed in the practice of States” and codification means “the more precise formulation and systematization of rules of international law in fields where there already has been extensive State practice, precedent and doctrine.”
Texts about the ILC are to be found at Internat 687.
The ILC's own publications are mostly in Official Papers (Floor 0 of the LawBod).