Runic inscription:

Otrygg and Bondi and Alvrik erected this stone after Kåre their father and Gunned after her farmer (her husband).

God help his spirit.

Torbjörn carved the runes.

+ Utrykr + auk + Buanti + auk + Alfrikr + raistu + stain + þinsa + eftiR + Kara + faþur + sin + auk + Guneþr + at + buanta + sin ·

Guþ hialbi (a)-- -ans

+ þurbiurn + hiuk ' runaR

Runecarcer:

Torbjörn skald (the poet)

The same Thorbjörn who carved U 29 Gerlög runestone, U 24 in Hilleshög church and U 15b in Ekerö church. According to "Runor" also U 20 in Färingsö church.

About Thorbjörn skald (the poet)

Thorbjörn the poet was probably a stubborn rune carver who thought it was easier with skaldic art than to create beautiful ornamentation, hard carved in granite. On this runestone U 37 we see, for example, how Thorbjörn normally makes his dragon heads.

Another detail that shows Thorbjörn's stubbornness is the leash between his neck and tail. On Thorbjörn's runestones, they are not properly tied, just applied as a loose marking.

An exception could be Gerlög's runestone U 29 which has an advanced ornamentation with two dragons that are intertwined in a correct way and has extra fine details such as the head and paws.
U 29 is signed with: Thorbjörn skald carved the runes.

But...
I absolutely believe that Thorbjörn carved the runes on U 29 and also created the inscription itself since he calls himself a "skald/poet/bard" but I don't believe that Thorbjörn created the ornamentation!

The ornamentation on U 29 is created by a skilled artist who knows the laws and rules of ornamentation, an artist who perhaps did not even carve in stone but worked with other materials such as wood, fabric, bone or silver.

I guess it was Gerlög herself who demanded a slightly higher quality of Thorbjörn's work.

About the Tingsite / Galghill

The place is today called Galgbacken, which is a medieval word. The two mighty runestones at the site show that this was something else during the Viking Age, a courthouse (Ting).  

In addition to the runestones at the site, the croft Tingstaden is located nearby. Since the words city and place have the same meaning, Tingsstaden/Tingstället is directly connected to the site, probably as a meeting place at the top of Igelviken, which was then a bay that reached all the way up to Tingsplatsen.

From the other direction in the north, one could similarly reach Tingsplatsen via Långtarmen and into the bay that led to what is today called Nora träsk. There are today Viking Age graves that belonged to a farm that in turn could very well have been a meeting place for those who came from the north and northeast.

The third direction is towards Hilleshög with the Viking-era farm Lisselby within sight of Ting site. If I guess correctly, the caretaker of the Ting site was in Lisselby, the person who looked after the site and made important preparations before the thing could begin.

The runestone fragment U 37b found in 2015 tells of someone who cares, and perhaps it was this very caretaker?

Links

Upplands runinskrifter > Page 50
(Only in Swedish)

Runor >  Riksantikvarieämbetet
(National Antiquities Board, mostly Swedish)

Google map > Find the runestone

 

ALL RUNESTONES

Ekerö municipality

ADELSÖ >
has 5 known runestones

BIRKA >
has fragments from 9 known runestones

MUNSÖ >
has 3 or 4 known runestones

EKERÖ >
has 11 known runestones

FÄRINGSÖ >
has 27 known runestones

LOVÖ >
has 8 known runestones