The concept of internal energy can be studied in many ways, but there is a common thread running through them. This thread originates in how the concept is derived - which is in applying the principle of the conservation of energy to structures in which energy is transferred by both heat and work to or from systems. In our study, we shall be combining together the notions of system, equilibrium, state, work and heat. The concept of internal energy enables a bridge to be made between work - familiar in mechanics - and heat, which we would tend to associate with changes of temperature. We will arrive at the First Law of Thermodynamics which relates together work, internal energy and heat, and study some problems in its interpretation in concrete cases.