Military strategy
One of these strategies was shown in the battle between Greek city states and Persia. The Battle of Thermopylae in which the Greek forces were outnumbered stood as a good military strategy. The Greek allied forces ultimately lost the battle, but the training, use of armor, and location allowed them to defeat many Persian troops before losing. In the end, the Greek alliance lost the battle but not the war as a result of that strategy which continued on to the battle of Plataea. The Battle of Plataea in 479 BC resulted in a victory for the Greeks against Persia, which exemplified that military strategy was extremely beneficial to defeating a numerous enemy.
Early strategies included the strategy of annihilation, exhaustion, attrition warfare, scorched earth action, blockade, guerrilla campaign, deception and feint. Ingenuity and adeptness were limited only by imagination, accord, and technology. Strategists continually exploited ever-advancing technology. The word "strategy" itself derives from the Greek "στρατηγία" (strategia), "office of general, command, generalship", in turn from "στρατηγός" (strategos), "leader or commander of an army, general", a compound of "στρατός" (stratos), "army, host" + "ἀγός" (agos), "leader, chief", in turn from "ἄγω" (ago), "to lead".  No evidence exists of it being used in a modern sense in Ancient Greek, but we find it in Byzantine documents from the 6th century onwards, and most notably in the work attributed to Emperor Leo VI the Wise of Byzantium.

Middle Ages: 

Genghis Khan and the Mongols: As a counterpoint to European developments in the strategic art, the Mongol emperor Genghis Khan provides a useful example. Genghis' successes, and those of his successors, were based on manoeuvre and terror. The main focus of Genghis' strategic assault was the psychology of the opposing population. By steady and meticulous implementation of this strategy, Genghis and his descendants were able to conquer most of Eurasia. The building blocks of Genghis' army and his strategy were his tribal levies of mounted archers, scorched earth-style methods, and, equally essential, the vast horse-herds of Mongolia.
Each archer had at least one extra horse—there was an average of five horses per man—thus the entire army could move with astounding rapidity. Moreover, since horse milk and horse blood were the staples of the Mongolian diet, Genghis' horse-herds functioned not just as his means of movement but as his logistical sustainment. All other necessities would be foraged and plundered. Khan's marauders also brought with them mobile shelters, concubines, butchers, and cooks. Through maneuver and continuous assault, Chinese, Persian, Arab and Eastern European armies could be stressed until they collapsed, and were then annihilated in pursuit and encirclement.
Compared to the armies of Genghis, nearly all other armies were cumbersome and relatively static. It was not until well into the 20th century that any army was able to match the speed of deployment of Genghis' armies. When confronted with a fortified city, the Mongol imperatives of maneuver and speed required that it be quickly subdued. Here the terror engendered by the bloody reputation of the Mongolians helped to intimidate and subdue.
So too did primitive biological warfare. A trebuchet or other type of ballista weapon would be used to launch dead animals and corpses into a besieged city, spreading disease and death, such as the Black Plague. If a particular town or city displeased the Mongolian Khan, everyone in the city would be killed to set an example for all other cities. This was early psychological warfare.
To refer to the nine strategic principles outlined above, the Mongol strategy was directed toward an objective (that schwerpunkt (main focus) being the morale and mental state of the opposing population) achieved through the offensive; this offensive was itself characterized by concentration of force, maneuver, surprise, and simplicity.

Early Modern era: In 1520 Niccolò Machiavelli's Dell'arte della guerra (Art of War) dealt with the relationship between civil and military matters and the formation of grand strategy. In the Thirty Years' War (1618-1648), Gustavus Adolphus of Sweden demonstrated advanced operational strategy that led to his victories on the soil of the Holy Roman Empire. It was not until the 18th century that military strategy was subjected to serious study in Europe. The word was first used in German as "Strategie" in a translation of Leo VI's Tactica in 1777 by Johann von Bourscheid. From then onwards, the use of the word spread throughout the West.
In the Seven Years' War (1756–1763), Frederick the Great improvised a "strategy of exhaustion" (see attrition warfare) to hold off his opponents and conserve his Prussian forces. Assailed from all sides by France, Austria, Russia and Sweden, Frederick exploited his central position, which enabled him to move his army along interior lines and concentrate against one opponent at a time. Unable to achieve victory, he was able to stave off defeat until a diplomatic solution emerged. Frederick's "victory" led to great significance being placed on "geometric strategy" which emphasized lines of manoeuvre, awareness of terrain and possession of critical strong-points.

Napoleonic: The French Revolutionary Wars and the Napoleonic Wars that followed revolutionized military strategy. The impact of this period was still to be felt in the American Civil War and the early phases of World War I.
With the advent of cheap small arms and the rise of the drafted citizen soldier, armies grew rapidly in size to become massed formations. This necessitated dividing the army first into divisions and later into corps. Along with divisions came divisional artillery; light-weight, mobile cannon with great range and firepower. The rigid formations of pikemen and musketeers firing massed volleys gave way to light infantry fighting in skirmish lines.
Napoleon I of France took advantage of these developments to pursue an effective "battle of annihilation". Napoleon invariably sought to achieve decision in battle, with the sole aim of utterly destroying his opponent, usually achieving success through superior maneuver. As ruler and general he dealt with the grand strategy as well as the operational strategy, making use of political and economic measures.

While not the originator of the methods he used, Napoleon effectively combined the relatively superior maneuver and battle stages into one event. Before this, General Officers had considered this approach to battle as separate events. However, Napoleon used the maneuver to battle to dictate how and where the battle would progress. The Battle of Austerlitz was a perfect example of this maneuver. Napoleon withdrew from a strong position to draw his opponent forward and tempt him into a flank attack, weakening his center. This allowed the French army to split the allied army and gain victory.
Napoleon used two primary strategies for the approach to battle. His "Manoeuvre De Derrière" (move onto the rear) was intended to place the French Army across the enemy's lines of communications. This forced the opponent to either march to battle with Napoleon or attempt to find an escape route around the army. By placing his army into the rear, his opponent's supplies and communications would be cut. This had a negative effect on enemy morale. Once joined, the battle would be one in which his opponent could not afford defeat. This also allowed Napoleon to select multiple battle angles into a battle site. Initially, the lack of force concentration helped with foraging for food and sought to confuse the enemy as to his real location and intentions.
The "indirect" approach into battle also allowed Napoleon to disrupt the linear formations used by the allied armies. As the battle progressed, the enemy committed their reserves to stabilize the situation, Napoleon would suddenly release the flanking formation to attack the enemy. His opponents, being suddenly confronted with a new threat and with little reserves, had no choice but to weaken the area closest to the flanking formation and draw up a battle line at a right angle in an attempt to stop this new threat. Once this had occurred, Napoleon would mass his reserves at the hinge of that right angle and launch a heavy attack to break the lines. The rupture in the enemy lines allowed Napoleon's cavalry to flank both lines and roll them up leaving his opponent no choice but to surrender or flee.
The second strategy used by Napoleon I of France when confronted with two or more enemy armies was the use of the central position. This allowed Napoleon to drive a wedge to separate the enemy armies. He would then use part of his force to mask one army while the larger portion overwhelmed and defeated the second army quickly. He would then march on the second army leaving a portion to pursue the first army and repeat the operations (defeat in detail). This was designed to achieve the highest concentration of men into the primary battle while limiting the enemy's ability to reinforce the critical battle. The central position did have a weakness in that the full power of the pursuit of the enemy could not be achieved because the second army needed attention. Napoleon used the central position strategy during the Battle of Waterloo.