Pay close attention to the subtitle: "A Political History from Independence to Occupation." The emphasis here should be on "Political History" - this book provides a good account of Iraq's national level politics in the 20th century, but contains very little coverage of the rest of the country during the period.
Chapters two through eight cover Baghdad politics between 1921 and 1958, and account for about two-thirds of the book. Three chapters cover the 1921-36 period, with Dawisha attempting to have one chapter be purely chronological while the other two are more topical, describing the attendant circumstances, such as the existence of protests in various parts of the countries or Sati al-Husri's pan-Arabist education/indoctrination programs. But because the details almost all related to happenings in Baghdad, there is a great deal of repetition of the same facts over and over, perhaps from a slightly different angle each time.
There is virtually no discussion of social, economic or religious currents, except to mention them in passing, but with insufficient detail for the reader to understand their importance. Significant in this regard is the historical development of the Shia clerical establishment, which played a key role in the 1920 revolt and was in stagnation after that point until 2003. Dawisha mentions the clerical role in 1920, several times, but explains nothing about the clerical establishment itself, its economic and social decline in the decades that followed (to explain why the 1920 events were not repeated until 2003), the importance of Iranian ties to the shrine cities during this time, or anything more than a passing reference to the great urban migration of the Shia poor, which has had such an important impact over contemporary events.
What Dawisha does well is explain why democracy failed in Iraq. The revolving door of the prime minister's office in the 1921-58 period, and the bizarre paradox of tolerant authoritarianism (elections were rigged, but political opposition leaders rarely faced a threat to their lives) during this period are explained well, and in a way that shows how the period paved the way for the nightmare that was to come. Dawisha poignantly points to how those who attempted to kill Abd al-Karim Qasim in 1959, including the young Saddam Hussein, were pardoned by 1961. Qasim would be killed in a coup in 1963, and when Saddam had his time to rule, no one who showed the slightest tendency toward opposition would live to coup another day.
The last three chapters cover three periods: 1958-1968 (the "Authoritarian Republic"/Abd al-Karim Qasim, Abd al-Salam Arif, Abd al-Rahman Arif), 1968-2003 (the Baathist/Saddam Hussein period) and the 2003-2007 period. The 1958-68 chapter is probably the most insightful of these. The Baathist period is mainly dominated by anecdotes of the horror of Saddam's rule, rather than a narrative. The eight-year Iran-Iraq war, which cost so many Iraqis their lives and changed the country forever, is covered in a single page. And it isn't until the book reaches 1980 that Dawisha mentions Muhammad Baqir Sadr and the Dawa Party, which Sadr helped found in 1958, and only then to report Baqir Sadr's murder by the regime. Quite a bit was happening in the interim that Dawisha passes over.
Dawisha's coverage of the post-2003 period broadly acceptable but there isn't much nuance. In discussing the Shia political parties, for example, he mentions four key parties - the Islamic Supreme Council of Iraq, Dawa, the Sadr faction and Fadhila - without discussing the ISCI-Sadr blood feud, that Fadhila is a branch of the Sadrist movement, or anything useful about the ISCI-Dawa relationship. The Sunni Awakening and the Iranian role in post-2003 period are very briefly discussed.
If you only plan to read one history of Iraq, read Charles Tripp's "History of Iraq" rather than this. But if you've read that and you want to know more, you could read this book for a better understanding of national politics, and the books of Yitzhak Nakash (buy "The Shiis of Iraq," NOT "Reaching for Power") and Mier Litvak on the Shia. I've written Amazon reviews on the latter two authors' books you may want to check out.