Battle of Yarmuk
With his massed cavalry force, he intended to drive the Byzantine cavalry entirely off the battlefield so that the infantry, which formed the bulk of the imperial army, would be left without cavalry support and thus would be exposed when attacked from the flanks and rear.
At the same time, he planned to push a determined attack to turn the left flank of the Byzantine army and drive them towards the ravine to the west.
Phase 1: Khalid ordered a general attack on the Byzantine front and galloped his cavalry around the left wing of the Byzantines. Part of his cavalry engaged the Byzantine left wing cavalry while the rest of it attacked the rear of the Byzantine left wing infantry. Meanwhile, the Muslim right wing pressed against it from the front. Under the two-pronged attack, the Byzantine left wing fell back and collapsed and fell back to the Byzantine left centre, greatly disordering it. The remaining Muslim cavalry then attacked the Byzantine left wing cavalry at the rear while they were held frontally by the other half of the Muslim cavalry, routing them off the battlefield to the north.
The Muslim right-wing infantry now attacked the Byzantine left centre at its left flank while the Muslim right centre attacked from front.
Phase 2: Vahan, noticing the huge cavalry manoeuvrer of the Muslims, ordered his cavalry to group together, but was not quick enough. Before Vahan could organize his disparate heavy cavalry squadrons, Khalid had wheeled his cavalry back to attack the concentrating Byzantine cavalry squadrons, falling upon them from the front and the flank while they were still moving into formation. The disorganized and disoriented Byzantine heavy cavalry was soon routed and dispersed to the north, leaving the infantry to its fate.
Phase 3: With the Byzantine cavalry completely routed, Khalid turned to the Byzantine left centre, which already held the two-pronged attack of the Muslim infantry. The Byzantine left centre was attacked at its rear by Khalid's cavalry and was finally broken.
Phase 4: With the retreat of the Byzantine left centre, a general Byzantine retreat started. Khalid took his cavalry north to block the northern route of escape. The Byzantines retreated west towards Wadi-ur-Ruqqad, where there was a bridge at Ayn al Dhakar for safe crossing across the deep gorges of the ravines of Wadi-ur-Ruqqad. Dharar had already captured the bridge as part of Khalid's plan the night before. A unit of 500 mounted troops had been sent to block the passageway. In fact, that was the route by which Khalid wanted the Byzantines to retreat all along.
The Byzantines were surrounded from all sides now.
Some fell into the deep ravines off the steep slopes, others tried to escape in the waters but were smashed on the rocks below and still others were killed in their flight. Nevertheless, many of the soldiers managed to escape the slaughter. Jonah, the Greek informant of the Rashidun army during the conquest of Damascus, died in the battle. The Muslims took no prisoners in the battle, but they may have captured some during the subsequent pursuit. Theodore Trithyrius was killed on the battlefield, and Niketas managed to escape and reach Emesa. Jabalah ibn al-Ayham also managed to escape and later briefly came to terms with the Muslims, but he soon defected to the Byzantine court again.

Aftermath: Immediately after the operation was over, Khalid and his mobile guard moved north to pursue the retreating Byzantine soldiers and found them near Damascus and attacked. Vahan, who had escaped the fate of most of his men at Yarmuk, was probably killed in the ensuing fighting. Khalid then entered Damascus, where he was welcomed by the local residents, thus recapturing the city.
When news of the disaster reached Heraclius at Antioch, the emperor was devastated and enraged. He blamed his wrongdoings for the loss, primarily referring to his incestuous marriage to his niece Martina.
He would have tried to reconquer the province if he had the resources but now had neither the men nor the money to defend the province any more. Instead, he retreated to the cathedral of Antioch, where he observed a solemn service of intercession. He summoned a meeting of his advisers at the cathedral and scrutinized the situation. He was told almost unanimously and accepted the fact that the defeat was God's decision and a result of the sins of the people of the land, including him. Heraclius took to the sea on a ship to Constantinople in the night.

His ship supposedly set sail, and he bade a last farewell to Syria,:Farewell, a long farewell to Syria, my fair province. Thou art an infidel's (enemy's) now. Peace be with you, O Syria—what a beautiful land you will be for the enemy's hands.Heraclius abandoned Syria with the holy relic of the True Cross, which was, along with other relics held at Jerusalem, secretly boarded on ship by Sophronius, Patriarch of Jerusalem, just to protect it from the invading Arabs. It is said that he had a fear of water, and a pontoon bridge was made for Heraclius to cross the Bosphorus to Constantinople. After abandoning Syria, he began to concentrate on his remaining forces for the defence of Anatolia and Egypt instead. Byzantine Armenia fell to the Muslims in 638–39, and Heraclius created a buffer zone in central Anatolia by ordering all the forts east of Tarsus to be evacuated.
In 639–642 the Muslims, led by Amr ibn al-A'as, who had commanded the right flank of the Rashidun army at Yarmuk, invaded and captured Byzantine Egypt.

Evaluation: The Imperial Byzantine commanders allowed their enemy to have the battlefield of his choosing. Even then, they were at no substantial tactical disadvantage. Khalid knew all along that he was up against a force superior in numbers and, until the last day of the battle, conducted an essentially defensive campaign, suited to his relatively limited resources. When he decided to take the offensive and attack on the final day of battle, he did so with a degree of imagination, foresight and courage that none of the Byzantine commanders managed to display. Although he commanded a smaller force and needed all the men he could muster, he had the confidence and foresight to dispatch a cavalry regiment the night before his assault to seal off a critical path of the retreat that he had anticipated for the enemy army.
Because of his leadership at Yarmuk, Khalid ibn al-Walid is considered one of the finest generals in history, and his use of mounted warriors throughout the battle showed just how well he understood the potential strengths and weaknesses of his mounted troops. His mobile guard moved quickly from one point to another, always changed the course of events wherever they appeared, and, then just as quickly, galloped away to change the course of events elsewhere on the field.
Vahan and his Byzantine commanders did not manage to deal with the mounted force and use the sizable advantage of their army effectively. Their own Byzantine cavalry never played a significant role in the battle and were held in static reserve for most of the six days. They never pushed their attacks, and even when they obtained what could have been a decisive breakthrough on the fourth day, they were unable to exploit it. There appeared to be a decided lack of resolve among the Imperial commanders, but that may have been caused by difficulties commanding the army because of internal conflict. Moreover, many of the Arab auxiliaries were mere levies, but the Muslim Arab army consisted for a much larger part of veteran troops.
The original strategy of Heraclius, to destroy the Muslim troops in Syria, needed a rapid and quick deployment, but the commanders on the ground never displayed those qualities. Ironically, on the field at Yarmuk, Khalid carried out, on a small tactical scale, what Heraclius had planned on a grand strategic scale. By rapidly deploying and manoeuvring his forces, Khalid was able to concentrate sufficient forces at specific locations on the field temporarily to defeat the larger Byzantine army in detail. Vahan was never able to make his numerical superiority count, perhaps because of the terrain, which prevented large-scale deployment.
However, Vahan never attempted to concentrate a superior force to achieve a critical breakthrough. Although he was on the offensive five out of the six days, his battle line remained remarkably static. That stands in stark contrast to the very successful offensive plan, which Khalid carried out on the final day by reorganising virtually all his cavalry and committing it to a grand manoeuvre, which won the battle.
George F. Nafziger, in his book Islam at war, described the battle:

Although Yarmouk is little known today, it is one of the most decisive battles in human history...... Had Heraclius' forces prevailed, the modern world would be so changed as to be unrecognizable.

Notes: ^ a: Modern estimates for Roman army:
Donner 1981: 20,000–40,000.
Nicolle 1994: (p. 32) Maximum 25,000 with an unstated number of Arab reinforcements.  (p. 65) 15,000–20,000.
Akram 1970: 150,000.
Kaegi 2003 (p. 242): 15,000–20,000, possibly more
Kennedy 2006 (p.