Robert Hogg was due to be sentenced at Dundee Sheriff Court after admitting targeting the woman between January and March this year.
The court heard previously that the woman had been left frightened by the content of the emails.
Sheriff Lorna Drummond QC issued a warrant for the 47-year-old's arrest.
Depute fiscal Stewart Duncan earlier told the court: "The complainer was using her laptop and noticed a large amount of emails in her junk mail folder.
"She opened the folder and found 500 emails from the accused.
"She opened several of them and was frightened by their content, some of which related to her studies, some was of a sexual nature and others referred to conversations she had with her father on Twitter."
The woman then blocked Hogg on the social networking site, but he sent her a further 25 emails in the next seven hours.
Some of those referred to the fact he had been blocked by her on the site.
The victim then contacted police who raided Hogg's home and seized two computer units.
They discovered all the emails had been sent from addresses attributed to Hogg and internet searches about her had been carried out.
Hogg had accessed her Twitter account several hundred times and saved various photos of her from her public profile into a folder under her name.
Mr Duncan said: "Some of the emails were of a sexual nature and some implied he had been watching her at her work."
Hogg, of Dundee, pleaded guilty at an earlier hearing to a charge of stalking the woman between 1 January and 25 March 25.
A cyber stalker who sent a woman more than 500 emails, some of a sexual nature, is being hunted by police after failing to turn up at court.