On Monday, insurgents set off seven car bombs, two of them at a Baghdad university, security officials said.
Five people died in the co-ordinated attack on the Mustansiriya University, and 25 were wounded.
A car bomb in the north Baghdad neighbourhood of Bab al-Muhaddam killed three people and wounded 25, while another in al-Tahrir Square city centre wounded 15.
Two car bombs went off within minutes of each other in east Baghdad, wounding nine. A seventh bomb exploded in the upscale Mansur neighbourhood, wounding seven.
Six people died in a series of shootings in south Baghdad's restive al-Dura district, while one civilian was killed near the restive city of Baquba, north of the capital.
Late on Sunday, police found the bodies of 15 young men near Abu Ghraib on Baghdad's western outskirts.
An interior ministry official said: "All the men had bullets in their heads."
The attacks come as Jawad al-Maliki, the prime minister-designate, starts the task of forming a national unity government that many see as the best way to avert civil war.