Maneuver warfare
Concepts: Although most battles between established armies have historically been fought based on attrition warfare strategies, many military doctrines and cultures are based on replete historical examples of maneuver warfare.
The view on attrition warfare involves moving masses of men and materiel against enemy strongpoints, with the emphasis on the destruction of the enemy's physical assets, success as measured by enemy combatants killed, equipment and infrastructure destroyed, and territory taken or occupied. Attrition warfare tends to use rigidly-centralized command structures that require little or no creativity or initiative from lower-level leadership (also called top-down or "command push" tactics).
Conventional warfare doctrine identifies a spectrum with attrition warfare and maneuver warfare on opposite ends. In attrition warfare, the enemy is seen as a collection of targets to be found and destroyed. It exploits maneuver to bring to bear firepower to destroy enemy forces. Maneuver warfare, on the other hand, exploits firepower and attrition on key elements of opposing forces.
Maneuver warfare suggest that strategic movement can bring the defeat of an opposing force more efficiently than simply contacting and destroying enemy forces until they can no longer fight. Instead, in maneuver warfare, the destruction of certain enemy targets, such as command and control centers, logistical bases, or fire support assets, is combined with isolation of enemy forces and the exploitation by movement of enemy weaknesses.
Bypassing and cutting off enemy strongpoints often results in the collapse of that strongpoint even where the physical damage is minimal, such as the Maginot Line. Firepower, primarily used to destroy as many enemy forces as possible in attrition warfare, is used to suppress or destroy enemy positions at breakthrough points during maneuver warfare. Infiltration tactics, conventionally or with special forces, may be used extensively to cause chaos and confusion behind enemy lines.
The retired officer and military theory author Robert Leonhard summarizes maneuver warfare theory as "preempt, dislocate, and disrupt" the enemy as alternatives to the destruction of enemy mass through attrition warfare.
Since tempo and initiative are so critical to the success of maneuver warfare, command structures tend to be more decentralized with more tactical freedom given to lower-level unit leaders. Decentralized command structures allows "on the ground" unit leaders but still works within the guidelines of the commander's overall vision, to exploit enemy weaknesses as they become evident, which is also called "recon-pull" tactics or directive control.
The war theorist Martin van Creveld identifies six main elements of maneuver warfare:

Tempo: as illustrated by John Boyd's OODA loop.
Schwerpunkt ('focal point'): the center of effort, or striking the enemy at the right place at the right time. According to van Creveld, ideally, a spot that is both vital and weakly defended.
Surprise: Leaving the enemy unable to counter an action is central to any maneuver, and may be achieved by their remaining unaware for as long as possible
Combined arms: the use of multiple means by which to attack the enemy creates an opportunity cost to any reaction. Should the enemy counter against one form of attack, they may leave themselves vulnerable to another. Additionally, different forms of attack may support each other through concurrent action (ex: Infantry supporting armor in such a way that the infantry has more available firepower, and the armor has protection from ambush)
Flexibility: a military must be well rounded, self-contained and redundant. By maintaining different avenues of attack, either in method, movement, or any other factor, alternatives are always available, and opportunities can always be seized
Decentralized command: rapidly changing situations may outpace the orders of a centralized command, leaving personnel with instructions that no longer apply. Lower levels of command must understand overall intent so as to adapt to a changing environment.

History: 

Early examples: For most of history, armies were slower than a marching soldier, making it possible for opposing armies to march around each other as long as they wished. Supply conditions often decided where and when the battle would finally start. Prehistorically, that began to change with the domestication of the horse, the invention of chariots, and increasing military use of cavalry. It had two major uses: to attack and use its momentum to break infantry formations and to use the advantage of speed to cut communications and isolate formations for later defeat in detail.
The retreat of the center of the Athenian and Platean citizen-soldiers (Hoplites) at the battle of Marathon against the forces of Datis in 490 BC, and subsequent pincer movements by Athenian forces on the flanks, used a similar tactic. The intention was to bring the Persian core forces forward—Persian and Saka axemen. The Hoplite flanks would then drive off their opposite numbers and enveloped the Persian center. Before the battle, Datis had re-embarked his cavalry—to which the hoplite formations had little real defense—which substantially weakened his position.
Khalid's invasion of Roman Syria in July 634—by invading Syria from an unexpected direction, the Syrian desert—is another example of taking enemy defenses by surprise. While the Byzantine army held the Muslim forces in southern Syria and had expected reinforcement from the conventional Syria-Arabia road in the south, Khalid, who was in Iraq, marched through the Syrian desert and entered northern Syria, completely taking the Byzantines by surprise and cutting off their communications with northern Syria.

Mongol use: The Mongol emperor Genghis Khan used a military system of maneuver warfare that focused on rapid, decisive maneuver, utilizing the skill and endurance of his Mongol horsemen. He used operational maneuver, command and control, deception, and precise battlefield tactics which were vastly superior to those of his opponents in China, Russia, Persia, and Eastern Europe and defeated virtually every enemy army that he faced.
An example of his usage of maneuver warfare was the defeat and annexation of the Khwarazmian Empire between 1219 and 1221 CE, which wielded an army nearly three times the Mongol army, in just a few months of fighting. The Mongol army's constant movement and maneuvering tied down the Khwarazmian forces, denying them the ability to gain the initiative as well as shocked and demoralized the Khwarazmian Shah Ala ad-Din Muhammad as well as his army, thus ending the campaign before the Shah could bring to bear his much larger numbers.

Napoleon's use: Similar strategies are also possible using suitably trained infantry. Napoleon I used preemptive movements of cavalry and fast infantry to interrupt the initial deployment of enemy forces. This allowed his forces to attack where and when he wanted, enabling force concentration, possibly in combination with advantage of terrain. It disabled effective coordination of enemy forces, even when they were superior in numbers. That was effective tactically and strategically.
During his time as a general and indeed his power base to become the head of France, Napoleon's reputation was based on a powerful and fluent campaign in northern Italy, opposing the numerically superior Austrians. He cited Henri de La Tour d'Auvergne, Viscount of Turenne as one major source of his strategy.
He trained a normal, if rather undisciplined, French Army of Italy into moving faster than most thought possible. That was partially because his army lived off the land and had no big logistical "tail." Both his ability to move huge armies to give battle where he wanted and the style of his choice would become legendary, and he was seen as undefeatable, even against larger and superior forces.
Napoleon also arranged his forces into what would be known in the present as "battle groups" of combined arms formations to allow faster reaction time to enemy action. That strategy is an important quality in supporting the effectiveness of maneuver warfare and was used again by Carl von Clausewitz.
Napoleon's principal strategy was to move fast to engage before the enemy had time to organize, to engage lightly while moving to turn the flank that defended the main resupply route, to envelop and deploy blocking forces to prevent reinforcement, and to defeat those contained in the envelopment in detail. All of those activities imply faster movement than the enemy as well as faster reaction times to enemy activities.
His use of fast mass marches to gain strategic advantage, cavalry probes, and screens to hide his movements; deliberate movement to gain psychological advantage by isolating forces from one another; and their headquarters are all hallmarks of maneuver warfare. One of his major concerns was the relatively slow speed of infantry movement relative to the cavalry.
It was that and subsequent defeats that caused a major doctrinal reevaluation by the Prussians under Clausewitz of the revealed power of maneuver warfare. The results of that review were seen in the Franco-Prussian War.

Mechanization: In the mid-19th century, various forms of mechanized transport were introduced, starting with trains running on steam power. That resulted in  significant logistic improvements. Opposing armies were no longer limited in speed by the pace of march. Some train-borne maneuvering took place during the American Civil War in the 1860s, but the sizes of the armies involved meant that the system could provide only limited support. Armored trains were among the first armored fighting vehicles employed by mankind.
During the Franco-Prussian War, the Prussians, knowing that the French could field a larger army than theirs, made a plan that required speed by surrounding the French strongpoints and destroying or bypassing them; it was called the Kesselschlacht, or 'cauldron battle'. The remainder of the army could advance unopposed to take important objectives.