No need to remind you that this description is from my own memory and I was so young to understand the situation correctly.
after the revolution in 1958, two of the leaders of the revolution shared the responsibility of leading Iraq. The first was Abdulkareem Qasim who had a higher position in the army, the second was Abdulsalam Aarif.
They were only few months after the revolution when the conflict started between the two, Qasim (supported by the communist) overcame the rule and put Aarif (supported by Arab nationalist and Baathist) in prison. Qasim started to take the side of the communists which had a strong organization in the south of Iraq. While in the north most of the people were Arab nationalist and against the communist. Another revolution started in 1959 in Mosul against Qasim. But it couldn't stand the large number of communist who were sent to mosul in the name of peace supporters. The revolution ended with a massacre, the communist with Qasim supporters used the Kurds and some villagers from outside Mosul to loot and spoil the city. Something that I didn't find an explanation to , is that, the Kurds and the Christians shared the communist in their crimes (that is the beginning of discrimination between different nationalities and religions), they killed all the rich peoples in the city, all the religious men and looted their houses, the city streets were filled with dead bodies, nobody dared to bury them. In short, the situation was worse than it is now during the American invasion to Iraq.
In 1963, another revolution started against Qasim, and that time, Aarif took control supported by the Baath party, and killed Qasim and became the president of Iraq. The baathist started gradually to overcome the situation, which forced Aarif to make another revolution to regain the control again and to get rid of the Baathies. Few months later, he died in an air-plain accident. His brother Abdulrahman Aarif become the president.
In 1968, Baathies started a revolution and took control over the government, Saddam was one of the leaders of the revolution. Ahmad Hasan Al-Baker become the president, and Saddam the vice president, but actually, he was the one who controlled the government.
In 1979, Al-Baker resigned and Saddam Hussein became the president of Iraq.
The end of the story is well known by all of you, I think!