Guerrilla Warfare
War fought by the weak against the strong through ambush, dispersal, and refusal to hold ground, named for Spanish irregulars fighting Napoleon.

The word is Spanish and it is a diminutive: guerrilla means little war. It entered English during the Peninsular War, when Napoleon put a French army into Spain in 1808, won every battle he cared to fight, and then discovered that winning battles had stopped mattering. Spanish irregulars ambushed couriers, cut supply columns, murdered stragglers, and vanished into villages that would not give them up. The French held the ground they physically stood on and nothing else. Napoleon later called Spain the ulcer that destroyed him, and the arithmetic supports him: he kept well over two hundred thousand troops there while fighting Russia.
The logic
Guerrilla war inverts the normal measure of success. A conventional army wins by destroying the enemy's forces and taking his territory. A guerrilla force has no territory worth taking and disperses rather than be destroyed, so the conventional army can win indefinitely without getting anywhere. Henry Kissinger put the asymmetry precisely in 1969, writing about Vietnam: the guerrilla wins if he does not lose, and the conventional army loses if it does not win.
The cost structure runs the same way. An ambush costs the insurgent a few men and some ammunition. Defending against ambushes everywhere costs the occupier a garrison in every village, which is why counterinsurgency ties down forces at ratios of ten or twenty to one.
Mao writes it down
Mao Zedong turned improvisation into doctrine in On Guerrilla Warfare in 1937 and On Protracted War in 1938, and every serious insurgent since has read him. His central claim was political rather than military: the guerrilla moves among the people as a fish moves through water. Without a population willing to feed, hide, and lie for you, guerrilla war is just banditry with a manifesto. That is why Mao's forces were obsessive about paying for what they took, a discipline his Nationalist opponents did not enforce.
Mao also insisted the guerrilla phase was temporary. His three stages ran from strategic defensive through stalemate to a conventional counteroffensive, because in the end you have to take the cities. Insurgencies that forget the third stage stay insurgencies forever.
What defeats it
Guerrillas do lose. The British beat the communist insurgency in Malaya between 1948 and 1960 by resettling half a million rural Chinese into guarded villages, cutting the insurgents off from the population, and pairing that with a credible promise of independence, so that the political case for fighting evaporated. The Americans copied the resettlement in Vietnam with the strategic hamlet program and did not have the political offer to go with it. Separation without a settlement produces resentment, not defeat.
The other reliable killer of insurgencies is a foreign sanctuary that closes. Guerrillas who can cross a border to rest and rearm are extremely hard to finish. Guerrillas who cannot, usually are.
Why it keeps winning
The record since 1945 is striking. France lost Indochina and Algeria, the United States lost Vietnam and eventually Afghanistan, the Soviet Union lost Afghanistan first. In each case the stronger power was undefeated in the field and went home anyway, because the insurgent's real target was never the army. It was the patience of the society that sent the army. Nuclear weapons and precision munitions have not changed this. They are irrelevant against an enemy whose main asset is time.