Military history
Chanakya's Arthashastra contains a detailed study on ancient warfare, including topics on espionage and war elephants.

Alexander the Great invaded Northwestern India and defeated King Porus in the Battle of the Hydaspes River. The same region was soon re conquered by Chandragupta Maurya after defeating the Macedonians and Seleucids. He also went on to conquer the Nanda Empire and unify Northern India. Most of Southern Asia was unified under his grandson Ashoka the Great after the Kalinga War, though the empire collapsed not long after his reign.
In China, the Shang dynasty and Zhou dynasty had risen and collapsed. This led to a Warring States period, in which several states continued to fight with each other over territory. Philosopher-strategists such as Confucius and Sun Tzu wrote various manuscripts on ancient warfare (as well as international diplomacy).
The Warring States era philosopher Mozi (Micius) and his Mohist followers invented various siege weapons and siegecraft, including the Cloud Ladder (a four-wheeled, extendable ramp) to scale fortified walls during a siege of an enemy city. The warring states were first unified by Qin Shi Huang after a series of military conquests, creating the first empire in China.
His empire was succeeded by the Han dynasty, which expanded into Central Asia, Northern China/Manchuria, Southern China, and present day Korea and Vietnam. The Han came into conflict with settled people such as the Wiman Joseon, and proto-Vietnamese Nanyue. They also came into conflict with the Xiongnu (Huns), Yuezhi, and other steppe civilizations.

The Han defeated and drove the Xiongnus west, securing the city-states along the silk route that continued into the Parthian Empire. After the decline of central imperial authority, the Han dynasty collapsed into an era of civil war and continuous warfare during the Three Kingdoms period in the 3rd century AD.
The Achaemenid Persian Empire was founded by Cyrus the Great after conquering the Median Empire, Neo-Babylonian Empire, Lydia and Asia Minor. His successor Cambyses went on to conquer the Egyptian Empire, much of Central Asia, and parts of Greece, India and Libya. The empire later fell to Alexander the Great after defeating Darius III. After being ruled by the Seleucid dynasty, the Persian Empire was subsequently ruled by the Parthian and Sassanid dynasties, which were the Roman Empire's greatest rivals during the Roman-Persian Wars.
In Greece, several city-states rose to power, including Athens and Sparta. The Greeks successfully stopped two Persian invasions, the first at the Battle of Marathon, where the Persians were led by Darius the Great, and the second at the Battle of Salamis, a naval battle where the Greek ships were deployed by orders of Themistocles and the Persians were under Xerxes I, and the land engagement of the Battle of Plataea.
The Peloponnesian War then erupted between the two Greek powers Athens and Sparta. Athens built a long wall to protect its inhabitants, but the wall helped to facilitate the spread of a plague that killed about 30,000 Athenians, including Pericles. After a disastrous campaign against Syracuse, the Athenian navy was decisively defeated by Lysander at the Battle of Aegospotami.
The Macedonians, underneath Philip II of Macedon and Alexander the Great, invaded Persia and won several major victories, establishing Macedonia as a major power. However, following Alexander's death at an early age, the empire quickly fell apart.

Meanwhile, Rome was gaining power, following a rebellion against the Etruscans. During the three Punic Wars, the Romans defeated the neighboring power of Carthage. The First Punic War centered on naval warfare. The Second Punic War started with Hannibal's invasion of Italy by crossing the Alps. He famously won the encirclement at the Battle of Cannae. However, after Scipio invaded Carthage, Hannibal was forced to follow and was defeated at the Battle of Zama, ending the role of Carthage as a power.
After defeating Carthage the Romans went on to become the Mediterranean's dominant power, successfully campaigning in Greece, (Aemilius Paulus decisive victory over Macedonia at the Battle of Pydna), in the Middle East (Lucius Licinius Lucullus, Gnaeus Pompeius Magnus), in Gaul (Gaius Julius Caesar) and defeating several Germanic tribes (Gaius Marius, Germanicus). While Roman armies suffered several major losses, their large population and ability (and will) to replace battlefield casualties, their training, organization, tactical and technical superiority enabled Rome to stay a predominant military force for several centuries, utilizing well trained and maneuverable armies to routinely overcome the much larger "tribal" armies of their foes (see Battles of Aquae Sextiae, Vercellae, Tigranocerta, Alesia).
In 54 BC the Roman triumvir Marcus Licinius Crassus took the offensive against the Parthian Empire in the east. In a decisive battle at Carrhae Romans were defeated and the golden Aquilae (legionary battle standards) were taken as trophies to Ctesiphon. The battle was one of the worst defeats suffered by the Roman Republic in its entire history.
While successfully dealing with foreign opponents, Rome experienced numerous civil wars, notably the power struggles of Roman generals such as Marius and Sulla during the end of the Republic. Caesar was also notable for his role in the civil war against the other member of the Triumvirate (Pompey) and against the Roman Senate.
The successors of Caesar—Octavian and Mark Anthony—also fought a civil war with Caesar's assassins (Senators Brutus, Cassius, etc.). Octavian and Mark Anthony eventually fought another civil war between themselves to determine the sole ruler of Rome. Octavian emerged victorious and Rome was turned into an empire with a huge standing army of professional soldiers.
By the time of Marcus Aurelius, the Romans had expanded to the Atlantic Ocean in the west and to Mesopotamia in the east and controlled Northern Africa and Central Europe up to the Black Sea. However, Aurelius marked the end of the Five Good Emperors, and Rome quickly fell into decline.
The Huns, Goths, and other barbaric groups invaded Rome, which continued to suffer from inflation and other internal strifes. Despite the attempts of Diocletian, Constantine I, and Theodosius I, western Rome collapsed and was eventually conquered in 476. The Byzantine empire continued to prosper, however.

Medieval warfare: When stirrups came into use some time during the Dark Ages militaries were forever changed. This invention coupled with technological, cultural, and social developments had forced a dramatic transformation in the character of warfare from antiquity, changing military tactics and the role of cavalry and artillery.
Similar patterns of warfare existed in other parts of the world. In China around the 5th century armies moved from massed infantry to cavalry based forces, copying the steppe nomads. The Middle East and North Africa used similar, if often more advanced, technologies than Europe.
In Japan, the Medieval warfare period is considered by many to have stretched into the 19th century. In Africa along the Sahel and Sudan states like the Kingdom of Sennar and Fulani Empire employed Medieval tactics and weapons well after they had been supplanted in Europe.
In the Medieval period, feudalism was firmly implanted, and there existed many landlords in Europe. Landlords often owned castles to protect their territory.
The Islamic Arab Empire began rapidly expanding throughout the Middle East, North Africa, and Central Asia, initially led by Rashidun Caliphate, and later under the Umayyads. While their attempts to invade Europe by way of the Balkans were defeated by Byzantium and Bulgaria, the Arabs expanded to the Iberian Peninsula in the west and the Indus Valley in the east. The Abassids then took over the Arab Empire, though the Umayyads remained in control of Islamic Spain.
At the Battle of Tours, the Franks under Charles Martel stopped short a Muslim invasion. The Abassids defeated the Tang Chinese army at the Battle of Talas, but were later defeated by the Seljuk Turks and the Mongols centuries later, until the Arab Empire eventually came to an end after the Battle of Baghdad in 1258.
In China, the Sui dynasty had risen and conquered the Chen dynasty of the south. They invaded Vietnam (northern Vietnam had been in Chinese control since the Han dynasty), fighting the troops of Champa, who had cavalry mounted on elephants. After decades of economic turmoil and a failed invasion of Korea, the Sui collapsed and was followed by the Tang dynasty, who fought with various Turkic groups, the Tibetans of Lhasa, the Tanguts, the Khitans, and collapsed due to political fragmentation of powerful regional military governors (jiedushi). The innovative Song dynasty followed next, inventing new weapons of war that employed the use of Greek Fire and gunpowder (see section below) against enemies such as the Jurchens.

The Mongols under Genghis Khan, Ögedei Khan, Möngke Khan, and Kublai Khan conquered most of Eurasia. They took over China, Persia, Turkestan, and Russia.