Adiabatic processes play a fundamental role in thermodynamics. In this chapter we discuss different definitions of such processes and some practical means by which they may be achieved for a fluid system. The General-Accessibility Axioms A–I to A–VI are upgraded to the Adiabatic-Accessibility Axioms AA–I to AA–VI which define the algebra of the adiabatic accessibility relationship \({\pmb {X}}\mathop {\prec }\limits ^{{{{\text { A}}}}}\,{\pmb {X}}'\) between states \({\pmb {X}}\) and \({\pmb {X}}'\) . The adiabatic work function and the First Law are defined with changes in internal energy given in terms of the work done on the system during an adiabatic process.