The victim is thought to have been dead inside the property for as long as three weeks, the time when she was last seen by her friends.
Police Scotland's major investigation team are carrying out door-to-door inquiries and speaking to the woman's neighbours.
Her body was found on Wednesday at a flat in Dobbies Loan Place, in the Townhead area of Glasgow.
Officers forced their way in and found the body inside.
Closed-circuit TV footage is also being examined as officers seek clues to the identity of her killer. They are describing the attack as unprovoked and are looking for a motive.
Sources said yesterday that despite the length of time between her disappearance and discovery of the body the inquiry was "progressing well".
Police have revealed the woman was seen on Wednesday October 9 and they are keen to establish her movements.
Detective Chief Inspector Colin Carey said: "We are trying to establish a motive for this attack as it appears to have been unprovoked.
"We know that the woman was seen on Wednesday October 9 and we need to establish her movements from then on, who she saw, where she went.
"So if anyone has any information please do get in touch with us."