History of the spread of Islam

Prophet Muhammad was succeeded by four leaders called Caliphs, regarded as rightly guided:  Abu Bakr, Umar, Usman and Ali. During their period of leadership, there were rebellions by some of the Arabian tribes, which they suppressed.  The superpowers of the day, Persia and the Byzantine - Eastern Roman Empire, challenged the emerging Muslim state.   The Muslims defeated the huge armies of Persia and the Byzantine - Eastern Roman Empire.  They went on to conquer Egypt, North Africa, Spain, and areas of Southern Russia, like Uzbekistan.

Like the conquest by the Israelites of the cities and lands of the Philistines with the permission of God, these conquests were to fulfill of the promises made to Hagar and Ishmael to make Ishmael a great nation, and the promise to Abraham regarding the son of the sacrifice, Ishmael, in Genesis 22:15-17, that his son's descendants would conquer their enemies.

World English Bible, Genesis 22:

22:15 The angel of Yahweh called to Abraham a second time out of the sky, 22:16 and said, “I have sworn by myself, says Yahweh, because you have done this thing, and have not withheld your son, your only son, 22:17 that I will bless you greatly, and I will multiply your seed greatly like the stars of the heavens, and like the sand which is on the seashore. Your seed will possess the gate of his enemies. 22:18 In your seed will all the nations of the earth be blessed, because you have obeyed my voice.”

Ishmael is the only son of Abraham who was ever the only son, and he too only till the birth of Isaac.  This promise to "possess the gate of his enemies" could be considered to be fulfilled either by Israelite conquest of the cities and lands of the Philistines, or by the world-sweeping conquests of the Ishmaelite Muslims, but it is the latter that better fulfills the prophecy, one that still holds true, a the following table shows:

The Ishmaelite Muslim civilization developed to be a great, world-dominating civilization, and it was special, unlike the Greek, Roman or other civilizations, in that it is the only great civilization that sprang from one of the sons of Abraham, for the Israelite Jews never became a great world-dominating civilization like the Ishmaelite Muslims.

Islam spread by trade and by preachers

But the Muslims were great traders and navigators, they traveled to farthest reaches of the world to trade in Indonesia and China, and where they went, they preached belief in the One God, and people believed.

There are hundreds of millions of Muslims in Indonesia and India today,  places where no Muslim army went, people converted to Islam of their freewill.  Forcible conversion is forbidden in Islam, and even in places conquered by Muslims, like India and Spain, the people were never forced to become Muslims, which is why today they are still Hindu or Christian.

Through the Muslims, many nations of the world have been blessed by coming into Islam, the religion of Abraham, again in fulfillment of the prophecy.

Developed knowledge

They Muslims brought back the knowledge of the ancient civilizations, from the Greek influence in Egypt, the Persian, the Indian, the Chinese.  They built on the knowledge and developed it further for centuries.

Superpower and center of world civilization

Between the Muslim states and sultanates, they were the superpower in the world for centuries, and the center of civilization from the year 700 CE till the beginning of their decline in 1500 CE.