Crimes include assaults and thefts – with two nasty town centre altercations during which victims were headbutted.
Police say images may be of both potential suspects or witnesses.
They add that members of the public should not approach anyone who they recognise from the photos.
Instead, they should contact Crimestoppers on 0800 555 111 and give the identity of the person shown.
They can also provide information anonymously using the Crimestoppers online form.
1. Man makes off with plush Helsinki Lay-Z Spa
This man was captured on camera leaving Ilkeston's Rutland Street Tesco bearing a luxury Helsinki spa, valued at £870 on May 18. Police said: "Male walks in, carries the spa and walks out." Photo: Derbyshire Police
2. Unknown male headbutts a known male in the face
This image relates to a public order offence on Ilkeston's Market Place on April 24. Police said "numerous altercations" ensued when a known female assaulted an unknown female. One of the assaults which followed included an "unknown male headbutting a known male in the face". Photo: Derbyshire Police
3. Victim headbutted on nose following town centre row
On May 5 outside Pizza Royal, Holywell Street, Chesterfield, a person was headbutted to the nose by unknown offender following an argument. Police would like to speak to the man pictured here. Photo: Derbyshire Police
4. Theft
This image has been published in connection with a theft at Spa Croft, Tibshelf Photo: Derbyshire Police