What controversy occurred after the death of the Prophet Muhammad?

Answer 1

After Muhammad's death, the question of succession led to disagreements and eventual factions in Islam. Following his death in 632AD, Muhammad's close companion, Abu Bakr, was named first calif. However, many disagreed with this appoinment, and believed that Ali, a relative of Muhammad, was his true successor. This controvery of succession is what eventually led to the division of Muslims into Sunni and Shia.

Answer 2

It was not real conflict but just different views. The proof is that after the next leader coming in power, both who were supporting and who were opposing came along together and supported the new leader. It was a process of true democracy, by the current terms.

The two different views were:

• The group, who are called later Shiites, believed that the Caliphs should only be within Prophet Muhammad descendants and family. Accordingly, they were supporting Ali Ibn Abou Taleb (Prophet cousin and the husband of his daughter Fatima) to be the first Caliph.
• The group, who were called Sunnis, agreed on the process of nominating Abou Bakr (after him Omar, then Ottoman, and then Aly) by the distinguished prophet followers (Sahaba in Arabic) and then getting approval of Muslims on the nominee (the process is called Moubaiy'a)

However, Shiites didn't protest or rise against the elected Caliphs (Abou Bakr, Omar, and Ottoman). Even Aly, himself, was good supporter and adviser to the three Caliphs until he was elected as the fourth Caliph.