This is /r/AskHistorians and this subreddit is reserved for questions on events before 1995. Unfortunately, your question doesn't fit in here.

But I will not leave you without an answer. You are looking for a general book on the war. If you're looking for one which is written by a historian, you are going to have to wait an additional 10 to 20 years before any serious historian will take on the monumental task to write about it. This does not mean, however, that there aren't any good books on the subject. At the present moment, Cobra II: The Inside Story of the Invasion and Occupation of Iraq as well as the follow up The Endgame: The Inside Story of the Struggle for Iraq, from George W. Bush to Barack Obama, both written by Michael R. Gordon and Bernard E. Trainor are deemed to be the best books on the subject.