What is the definition of the sciences of Usul al-Fiqh and Usul al-Hadith, and what are their scopes?

Principles of Islamic jurisprudence (Usul al-Fiqh) are defined in two ways: First, by its individual components (Usul and Fiqh). Usul is the plural of Asl, which means that upon which something else is built. Fiqh literally means understanding, and technically refers to the knowledge of practical Sharia rulings derived from their detailed evidence. Second, as a specific discipline, it is a science that investigates the general evidences of Fiqh, how to benefit from them, and the state of the beneficiary.

As for the principles of Hadith (the science of Hadith terminology), it is a science comprising rules by which the conditions of the isnad (chain of narration) and the matn (text) are known, in terms of acceptance or rejection.