What were the disagreements that occurred between the Rightly Guided Caliphs after the death of the Messenger, may Allah bless him and grant him peace, regarding the succession to the Caliphate?

The Messenger of Allah, peace and blessings be upon him, passed away on a Monday in Rabi' al-Awwal, during the forenoon (Duha) time. He was buried on Wednesday night, at midnight. His burial was delayed for several reasons, including: the Companions praying over him individually without an Imam, their disagreement concerning his washing ritual and his burial place, and most importantly, to unite the word of the Ummah and protect it from the disunity that nearly afflicted it. A dispute arose among the Companions after his death concerning his passing, and it was resolved by the sermon of Abu Bakr Al-Siddiq, may Allah be pleased with him, after which they pledged allegiance to him in the Saqifah and the Mosque. Indeed, his death, peace and blessings be upon him, was a momentous event that profoundly affected the Companions.