Internal energy
The total microscopic energy stored in a system — the sum of its molecules' kinetic and potential energies — and the only quantity a body genuinely 'contains'.
Definition
Internal energy, written U, is the grand total of all the microscopic energy held in a system: the kinetic energy of its molecules as they translate, rotate, and vibrate, plus the potential energy of the forces between them. It excludes the bulk kinetic energy of the system as a whole and any external potential energy — it is the energy seen from a frame riding along with the body. For an ideal gas, where intermolecular forces vanish, U depends only on temperature.
Internal energy is a state function: it depends solely on the present state of the system (its temperature, pressure, and volume) and not at all on the path by which that state was reached. This is what makes U the only legitimately 'stored' thermal quantity. Heat and work, by contrast, are not stored — they are energy in transit across the system boundary, and it is meaningless to ask how much heat or work is 'in' a body.
The change in internal energy is governed by the first law of thermodynamics, ΔU = Q − W: it rises when heat is added and falls when the system does work on its surroundings. Because U is a state function, ΔU between two states is fixed even though the heat and work that produced it are not, and over any complete cycle ΔU returns to zero.