Crossovers/Events/Major Stories:
#1-6 - Extremis
#7-12 - Execute Program
#13-14 - Civil War
#15-18 - Director of S.H.I.E.L.D.
#19-20 - World War Hulk
#21-28 - Haunted
#29-32 - With Iron Hands
#33-35 - War Machine: Weapon of S.H.I.E.L.D.
Title's official name:
During its run, the title had a confusing official name. From its first issue, the adjective "Invincible" preceeded "Iron Man" on the cover, though its indicia only stated "Iron Man." The indicia eventually changed to "Invincible Iron Man" with #17. However, two issues earlier with #15, the subname of "Director of S.H.I.E.L.D." had been added to the cover. The indicia later changed to reflect this, though not until #29. The final three issues of the title (#33-35) was rebranded "War Machine: Weapon of S.H.I.E.L.D." though the indicia did not change.
Name of title by cover:
#1-12: Invincible Iron Man
#13-14: Iron Man
#15-32: Iron Man, Director of S.H.I.E.LD.
#33-35: War Machine, Weapon of S.H.I.E.LD.
Name of title by indicia:
#1-16: Iron Man
#17-28: Invincible Iron Man
#29-35: Iron Man, Director of S.H.I.E.LD.
Although this is open to interpretation, for the sake of simplicity, this site considers the title in its entirety to be Iron Man (4th series).