The groom's column reads:

Transcription ( "|" indicates a new line): "Ungkarl Hans Jørgensen | 30 Aar gammel, Født i Herløv | d. 6te Mai 1841. Snedker og huuseier | i Katfield i Amerika | (Minnesota)| vacc: 6 Juli 1842 af Districtslæge Toft."

Translation: "Bachelor Hans Jørgensen 30 years old, born in Herløv the 6th (of) May 1841. Cabinet maker and houseowner in Katfield (Chatfield) in America (Minnesota). Vaccinated [for smallpox] 9 July 1842 by District doctor Toft [the name of the physician who performed the vaccination. All couples had to prove they had been vaccinated for smallpox before they could get married]." See this article in the FamilySearch Wiki about vaccinations in Denmark: https://www.familysearch.org/en/wiki/Vaccinations_in_Denmark https://www.familysearch.org/en/wiki/Vaccinations_in_Denmark

The bride's column reads:

Transcription: "Pige Anne Marie Christensen, 22 | Aar gammel, født i Hennetved d. 8 April | 1849, Pleiedatter of Gaardeier Kjærs Enka i Stæv | ne. vacc: 21 July 1849 af Districtslæge Toft"

Translation: "Maid Anne Marie Christensen, 22 years old, born in Hennetved the 8 April 1849, fosterdaughter of farm owner Kjær's widow in Stevne. Vaccinated 21 June 1849 by District doctor Toft."

Nicoline Christine Nielsen is written in by mistake. She is actually the bride in the next record on the next page of the book.

The next column lists the "bondsmen" - see this article in the FamilySearch Wiki on Nordic Engagement and Marriage Records: https://www.familysearch.org/en/wiki/Nordic_Engagement_and_Marriage_Records#:~:text=In%20Scandinavia%2C%20the%20engagement%20comes,in%20the%20early%20church%20records. https://www.familysearch.org/en/wiki/Nordic_Engagement_and_Marriage_Records#:~:text=In%20Scandinavia%2C%20the%20engagement%20comes,in%20the%20early%20church%20records.

They are Christen Jensen Nielsen, a cottager in Statene and Hans Johansen (Iversen) of Stevne.

The next two columns state that the marriage was performed 27 July in Lindelse church - so they were married in Lindelse, Svendborg, Denmark.

The next to last column lists the page number and entry number of the couple in the Jevnførelses Register (Comparing Index). The groom is on page 791, entry 75 (here: https://arkivalieronline.rigsarkivet.dk/da/billedviser?bsid=507451#507451,88996932 Arkivalieronline - Rigsarkivet ) and the bride is on page 907, entry 11 (here: https://arkivalieronline.rigsarkivet.dk/da/billedviser?bsid=515664#515664,89357966 Arkivalieronline - Rigsarkivet ). Both of these entries point to their individual birth and confirmation records if you are interested in looking for that information.

The final column indicates that they had permission to marry with a "royal letter" of the 25th of July 1871. I am not sure why that was needed-perhaps because he wasn't living in Denmark at the time.