Short answers, pulled from the story.
Energy is the quantitative property transferred to a body or physical system, recognizable in the capacity to do work and in the form of heat and light. It is a conserved quantity that can be converted in form but never created or destroyed.
The SI unit of energy is the joule, a derived unit equal to the work done in applying a force of one newton through a distance of one meter. A kilowatt-hour equals 3.6 million joules, and other units used in specific fields include the erg, foot-pound, electronvolt, food calorie, kilocalorie, and BTU.
The word energy derives from the Greek energeia, which possibly appears for the first time in the work of Aristotle in the 4th century BC. At that time it was a qualitative philosophical concept broad enough to include ideas such as happiness and pleasure.
Émilie du Châtelet proposed conservation of energy in the marginalia of her French translation of Newton's Principia Mathematica in the early 18th century, the first formulation of a conserved measurable quantity distinct from momentum. James Prescott Joule discovered the link between mechanical work and heat in 1845, and William Thomson, known as Lord Kelvin, helped formalize the law within thermodynamics.
All forms of energy sort into kinetic energy, set by motion, and potential energy, the stored capacity for motion based on position in a field. Named forms include chemical, elastic, electric, gravitational, magnetic, nuclear, radiant, thermal, mechanical, and rest energy, and these are not mutually exclusive.
Albert Einstein's 1905 theory of special relativity showed that rest mass corresponds to an equivalent amount of rest energy, given by E equals mc squared. Because the speed of light squared is so large, one kilogram of rest mass is equivalent to 21.5 megatonnes of TNT.
According to Noether's theorem, stated in 1918, conservation of energy is the direct mathematical consequence of the translational symmetry of time. Because the laws of physics do not change from one moment to the next, the total energy of a system stays constant.