Scattered around Zealand and the surrounding islands, many runestones have been found. Unfortunately, former generations did not have any respect for them, or they actually feared them. That meant many have gone missing over the centuries. Some have been used as they were, as foundation to churches and mansions, others have been broken up to be used in the walls.
Many of those left have, paradoxical enough, been saved by the local churches. That said, it must be mentioned; some actually bear crosses, and was raised in the Christian God's name.
They have been made over a long period, and the letters used on them have evolved. It started in the first century, and was mainly used by Germans and the Nordic people until around 1300.
The runes were created to epigraphic texts, and was used in both religious and everyday contexts like memorial to deceased, owner signatures on objects, graffiti, letters, notes, verses (of poetry), prayers, short spells, etc.

They have evolved in three stages, where the Elder Futhark were in use from the first century to the eights. It contained 24 runes, while the younger is reduced to 16.
The Anglo-Saxon Futhorc, used from 400 to 1100, and the Younger Futhark, used from 800 to 1100. The Younger Futhark is divided further into the long-branch runes (also called Danish, although they were also used in Norway and Sweden); short-branch or Rök runes (also called Swedish-Norwegian, although they were also used in Denmark); and the stavlösa or Hälsinge runes (staveless runes).
The Younger Futhark developed further into the Medieval runes, used 1100 to 1500 AD, and the Dalecarlian runes from around 1500 to 1800 AD. They were used alongside the Latin alphabet, which become the most common.

Their origin is unknown, but it is thought they could have been inspired by the Latin letters, but made more suitable for easy carving into tree, metal or stone. Most of the old ones are known from Denmark, but as the wood probably was the most common in the old days, most have vanish by time. The runestones only become popular in the sixth century. The moist and frosty winters in Denmark are not kind to these old stones.
I have visited all of the stones around the islands, and made a page for each with breath information.