IslamArabia in the 7th century. People who believe in Islam are called Muslims.
Muhammad lived in Mecca, a place with Christians, Jews, and Animists, where a shrine to Abraham was located. He was a civic leader and businessman who had a vision at about the age of 40. He accepted that the texts used in the other religions were good and led to good behavior when properly applied, but his vision was very specific and Muslims believe it over-rides what Christians call the Bible:
The Qur'an is an exact literal transcription of elements of the vision he dictated over many years, which (like a film) did not materialize in the order in which it is written. The methods of justice and jurisprudence ("fiqh") and form of government associated with Islam have been interpreted many ways in many cultures. This interpretation is called "al-urf". See a list of Islamic terms in Arabic for other terms that have very specific meanings to Muslims and in Islam. Muslims do not accept translation of the Qur'an out of Arabic - and tend to prefer the Arabic words for meanings within Islam.
Muslims by definition are obligated to take a very diligent attitude to scientific and judicial investigation. In courts and politics fairness is assumed to rely on some process of investigation called "ijtihad" for "independent thought". Many historians consider this to have led to what we now call the scientific method. From its 7th century founding to about the 13th century when the Mongols sacked Baghdad or 1492 with the loss of Muslim Spain, Muslim thought and science was considered to lead the world. See early Muslim philosophy for more on this.
These traditions languished under the Ottoman Empire which dominated Arabia from the 16th century to the early 20th century. They continued to a greater degree in Africa and Indonesia but without much guidance from the traditional centres of thought. Today, with modern communications and new ambitions of Islamic peoples, the most useful of the traditions are being revived strongly. See Islam as a political movement and Modern Islamic philosophy for more on this.
Islamic economics forbids odious debt and exploitation based on debt. It is one of many areas where Islamic ideas are being revived in modern contexts and applied to modern problems.
Muhammad was the final Prophet of Islam - although Islam recognized Jesus Christ, Moses, Abraham, Noah and Adam also as prophets, and recognized that other prophets had come to other peoples.
There are about one and a half billion Muslims in the world. The Muslim world is often referred to as having one way of looking at things, although this is a very great simplification.
A mosque is a place where Muslims worship but also discuss religious and political matters. A more specialized school for teaching and discussion only is called a madrassa, and the modern university emerged from a more specialized theological school called a jamia. The world's oldest university, in Cairo, is still devoted primarily to Islamic study.