Higgins, who won the World Snooker Championships in 1972 and 1982, was found dead in his flat in the Sandy Row area of Belfast on Saturday.
He had suffered from throat cancer for 10 years and he also suffered from a long-term addiction to alcohol.
The mayor led tributes to the sporting great. Mr Eastwood said: “Alex Higgins was a fantastic snooker player who contributed to putting the sport of snooker on the |international stage. He was one of the great characters and he will be fondly remembered for his unique style of play and colourful life.”
Pat Moore, proprietor of North West Snooker and Pool, said Alex Higgins had brought a spark to the game that had enthused a generation.
He said: “He was fantastic, the type of colourful character he was he never went with the norm. He was a rebel and there was no doubting the personality he brought to the game. People like to watch the flamboyant players. There have been too many robots in the past 15 years and the game is struggling to get young people involved and excited.
“I remember when Alex Higgins won the Word Championships in 1982 and did a tour with Jimmy White. We actually watched them at the Sports Complex at Templemore.”
Mr Moore said he met Jimmy White about six weeks ago in Buncrana and was told that they had raised around £15,000 during a fundraiser in Manchester to help Alex pay for dental treatment so he could eat. Mr Moore said he was told by Mr White that the World Snooker Association had also pledged to help Alex.
The book of condolence will be open from 9-5pm at the Guildhall until Friday.
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