All three of the attacks were carried out in the closes of flats over the period between 31st December and 3rd of February after the women were followed in to the communal area of the tenements.
The attacks occurred on Great Western Road, Arlington Street and Kersland Street, all within a 1.5 mile radius of the West End and University of Glasgow campus.
The suspect has been described as white, between 20 and 30, between 6ft and 6ft 2 inches tall, and slim with black hair. He has been noted to have been wearing a hooded top and black or dark trousers, with a black beanie in two of the assaults and a black skip cap in one of them.
Chief Inspector Alan Gibson, of Strathclyde Police, said on Tuesday: "Each of these incidents were particularly frightening for the young women concerned. We are continuing enquiries in the local area including viewing all available CCTV in an effort to identify the man responsible, and we have been deploying extra officers around the area to provide public reassurance."
A spokesman for the University said: "The safety of staff and students is always of the utmost priority. Whilst crime is thankfully rare on or near campus we would urge that some simple steps are followed to minimise any danger. These include, keeping to well lit areas and where possible to avoid travelling alone. If you have any concerns at any time, approach a member of University staff or contact the police."
Personal attack alarms are available for free at the SRC Advice Centre.
Strathclyde Police have also requested that anyone who has seen a man fitting the description of the suspect contact them on 0141 535 3350.