The delivery of Covid-19 vaccines began on December 8 with vaccinators, followed by residents and staff in care homes from December 14.
Now the next step has begun with the routine vaccination of all those over 80.
The first GP practice to take up the programme was the Pentlands Medical Centre in Currie, Edinburgh.
John Elphinstone, 91, was among the first to be given the vaccine, by Practice Nurse Marianne Stewart.
Mr Elphinstone said he was feeling “very pleased” after being given the dose.
"My family were quite excited when I told them I would be getting it,” he said.
“More excited than me I suppose. They’re always anxious about me when I go out and about or to the shops, and this will give me some protection.”
His vaccination will be a “relief” to his family, and to Mr Elphinstone himself.
"All through the past months I’ve been fine, but recently I’ve got more anxious because I know we’re quite near to getting treatment and it would be terrible to get caught up in it now.”
Practice Nurse Marianne Stewart said it was “really good to get started” with the programme.
"The more we can do, the more people who feel protected, hopefully it will take away some anxiety, as a lot of our patients do get quite anxious, even just coming into the practice – although we keep it as safe as we can.
"Hopefully by doing the first vaccines initially that will help them feel a little bit more comfortable.”
The vaccination programme will be extended to all practice members over 80, with capacity to vaccinate 100 people a week.
The practice serves around 800 local people over 80, staff said.
Other GP practices will be given vaccination stocks proportionate to population.
The Scottish Government is following the vaccination priority list determined by the four-nation Joint Committee on Vaccination and Immunisation (JCVI), with all those over 50 and others with underlying health conditions considered to be in the first priority group.
Nicola Sturgeon has said she hopes to offer a vaccine to all of this group by early May.
So far more than 100,000 first doses have been administered in Scotland.