A 29-year-old man was attacked in Drumchapel by a group of men as he walked along the road with two friends in the early hours of Saturday.
He was seriously assaulted during the incident on Peel Glen Road, which happened around 1.35am.
Investigations are ongoing, with officers carrying out door-to-door inquiries in the area in a bid to uncover more information about what happened.
They are also reviewing CCTV images of the area, which they hope may reveal further clues.
At present there is no description of the men police are hunting for, but it is understood that they fled in a silver car towards Kinfauns Drive.
Detective Sergeant Andy Gibson, Drum-chapel CID, said today: "The injured man sustained serious head injuries and is in a serious condition in hospital.
"His friends were not injured and we are trying to piece together the circumstances surrounding the attack - was he the intended target for example?
"Our inquiries are at an early stage and I would appeal to anyone who was in the area to contact Drumchapel CID on the non emergency number 101.
"The weather was good on Friday night into Saturday morning and, it is possible people were still out and about or up at this time.
"There was a party in the street and while there is no indication that any of the people involved in the assault were there, revellers may have seen or heard something that will help us."
Anyone with information can also contact Crimestoppers anonymously on 0800 555 111.