How far back do you want to go, and how much do you know about Middle Eastern history in general? A good starting point is always The Arabs: A History, by Eugene Rogan.

To learn the history of Iraq, you need to know about what led to its creation. Iraq was part of the Ottoman Empire for 400 years; it was through Basra that the British invaded the Ottoman Empire in the First World War. The Arab Revolt against the Ottomans was led by the Hashemites, who were promised a country comprising all the Arab lands (but the British made conflicting deals with France and promises to the Jewish community). Near the end of the war, Emir Faisal of the Hashemites declared a new Arab kingdom in Syria based from Damascus. The French removed him from Syria, and soon after (1921), the British turned him into King of Iraq, which had newly been made a colonial mandate of Britain. Hashemite kings were also established in the new Mandate of Transjordan and in the Kingdom of Hejaz (western Arabia, conquered by Ibn Saud in the 1920s).

Iraq's history was from its beginning then tied to colonialism, Britain and the new concept of Arab Nationalism - which Iraq was an early adopter of, in part because King Faisal, as a non-Iraqi Arab, needed some new ideology to build his legitimacy and tie his nascent country together. This was never a fully successful ideology because Iraq contained a substantial non-Arab minority, particularly Kurds, who made up 20% of the population and were concentrated in the oil-rich north of the country (the oil fields of Mosul were important to colonial interests from an early stage). After the revolutions toppling monarchies in Iraq and Egypt in the 1950s and the rise of the Baathists, Arab nationalism grew as a force, as these developments would directly lead to Saddam Hussein's eventual rise to power (Hussein would style himself using Pan-Arab language as well).

This is just a quick sketch of the history, meant to illustrate that to understand the history of Iraq, you also need a grasp of Middle Eastern history in general. The Arabs provides that handily, and is the most accessible resource on 20th modern Arab history in recent years.

When you're done with that, there are several histories of Iraq that you can look at. I'd recommend A History of Iraq by Charles Tripp. It's by a leading scholar in the field and is a good start into the subject.