Asymmetric warfare is defined as an unconventional engagement where a traditional army faces an insurgency or low-intensity guerrilla army.
A symmetric conflict would have been, for example, the US versus the Soviet Union in the cold war. Both armies were similarly composed of armored divisions, infantry and support. Tactics could be expected to be somewhat similar (allowing for differences in doctrine). The tools with which they waged were at least equivalent.
Against rebel or insurgency groups, however, engagement is different. Al-Q'aida doesn't have main battle tanks or artillery; they have Improvised Explosive Devices (IEDs), suicide bombers and death squads.
Asymmetric warfare means a traditional army facing off against a decentralised force (often called 'networked' force). The obvious difficulties are that the traditional army (e.g. the USA) cannot just deploy tanks, because their opponents aren't an army in uniform who they can shoot at.
It requires a different approach and different tools.
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Biological warfare.
trench warfare chemical warfare
trench warfare
Maneuver warfare is highly mobile warfare such as a tank battle.
World War 1 introduced aerial warfare with airplanes and trench warfare