Nicola Sturgeon declared the SNP has "made history" by winning a third term in government at Holyrood but the party failed to reach a majority.
The Scottish Conservatives had their best ever result, securing 31 MSPs, while Labour suffered its worst result since devolution with 24 MSPs.
SNP leader Nicola Sturgeon has confirmed she will not seek to form a coalition with another party.
The SNP (Scottish National Party) fell two seats short of an overall majority - winning 63 of 129 seats available - but with such a "large group of MSPs elected", Ms Sturgeon said she saw no need to seek a "formal arrangement".
Instead, she said, when the Scottish Parliament reconvenes in the coming days, she would ask them to formally re-elect her as First Minister, and she will then form a minority SNP government.
"We won a clear and unequivocal mandate, and I secured the personal mandate I sought to implement the bold and ambitious programme for government that I asked the country to vote for," she said.
On the question of independence, she added, the SNP would make their case " with passion, with patience and with respect", saying their aim was to "persuade, not to divide".
She said she had a "duty" to "rise above party politics", and to govern in the best interests of all of the country as a whole.
21-year-old Ross Greer has been elected as the youngest-ever Member of the Scottish Parliament (MSP), representing the Green Party.
Labour is facing a disastrous election night in Scotland, with the party in danger of finishing third behind the SNP and the Conservatives.