The Muslim empire spread out of mecca, east to India, west across north Africa and on into Spain and almost into France but there were people there that held them off.
There were many military conquest and took about 100 years to expand most of there empire. They were great fighters because they believed that if they died in battle for there empire they would go strait to heaven this was also called a jihad or holy war. But they also treated the people they conquered better than there previous rulers before.
They had the battle of tours in southern France. The French Christians, under Charles Martel, defeated the Muslims and stopped their advanced into Europe. They also had a golden age that was 700-900A.D.
There contributions to our society now are they spread Gupta math idea and created algebra and trigonometry. They also created hospitals and wrote medical text books they also required that doctors have to pass exams to practice medicine. There architecture was influenced by byzantine by Indian styles. There was also made the astronomical tables. The Islamic laws becomes the basis for political laws in the empire. They also had money and created a credit system. They also preserved the Greek and roman cultures.