Ten of thousands of people are still without electricity or water following devastation caused by Storm Ophelia.
Irish Water has said there are 48,000 customers still without water following damage caused by the extreme weather.
Cork and Waterford are the worst affected counties.
The faults were generally as a result of power failures are treatment plants and pumping stations and burst pipes during the historic storm.
However, it is feared that gale force winds this weekend will halt restoration efforts.
This morning, schools have re-opened and transport services have resumed.
Irish Water is currently co-coordinating up to 30 water tankers to affected areas , and in many places generators are keeping water plants in operation.
A further 23 generators on route to assist to restore supplies to 64,000 in the most impacted areas, particularly around the south of the country.
A number of wastewater treatment plants and a significant number of sewage pumping stations where power failure is resulting in discharge of untreated or partially treated wastewater to receiving waters.
Around 30 wastewater treatment plants are also without power.
A crisis management team will stay in place at the utility until full service resumes.
Gerry Grant of Irish Water said he is "very hopeful" that progress will be made in fixing services - but they are largely dependent on ESB's ability to restore power.
Householders are being asked to conserve water until the issues have been resolved.
It comes as the ESB reported a number of "near misses" involving front-line staff who are trying to repair power lines.
The National Emergency Coordination Group heard crews had escape injuries from falling trees and live wires.
Derek Hynes of ESB appealed to he public to remain "vigilant, stay safe and stay clear".
Some 130,000 are still without power as ESB crews are prioritising water plants as repair work continues following Monday's extreme weather.
The utility is hoping to have power restored to those people still without power over the next three to four days.
Due to the devastation caused by fallen trees nationwide and because of the rural location of some of those affected it will take time to get services restored to those who still have no electricity she said.
Storm Ophelia caused the largest event ever faced by the utility with some 360,000 people left without power due to the storm which wreaked havoc across Ireland on Monday.
"We are hopeful that the majority of customers in the Northwest and Dublin will be restored tonight. We are also making significant progress in counties Kerry, Laois, Galway, Clare and Westmeath. The southwest counties of Cork and Kerry have had power restored to over 100,000 customers," the ESB said.
"We will have estimated restoration times for those customers who remain without power in the morning. ESB Networks will contact vulnerable customers without power this evening to provide updates on likely restoration times."
Luas Red and Green Lines have returned to passenger service ahead of schedule.
"Following a test of the track and technical systems tonight a decision was made to open service in advance of the publicised opening time Wednesday" the company said in a statement.
Meanwhile Met Eireann's Evelyn Cusack has indicated that another, much weaker storm named Brian could hit at the weekend.
She said there is a "huge question" over whether it will impact on Ireland but suggested that even if it does there is no concern that it will be anything like Ophelia.
Ms Cusack said that at present there are plans to issue a fresh weather warning.
An estimated 110,000 people are without communication services following unprecedented Storm Ophelia.
It is also feared that more customers will lose their broadband, telephone and mobile services today.
They said the storm caused unprecedented and widespread levels of damage to eir’s infrastructure, including damage to poles and cables. They marked the southwest and the midlands as the worst affected areas, in particular Cork County.
Current fault levels for specific counties include:
The national clean-up bill is expected to run into the tens of millions.
Following a National Emergency Coordination Group, its chairman Sean Hogan said: "There will be dangers even after the wind has passed.
"Unfortunately this storm has left tragedy in its wake and we extend our sympathies to these families."
He said the "next stage is now underway" and clean up crews are already on the ground in parts of the country.
Mr Hogan said the decision to effectively close down the country for the day by issuing a red alert weather warning was taken "based on the best scientific advice".
He said Met Eireann has entered "unchartered territory" but the emergency group was in no doubt that it was the correct decision.
"People should not take any risks over the coming days," Mr Hynes said, adding there are 5,000 individual faults.
The HSE have warned patients to expect "some disruption" this week as they deal with a backlog of cases. Some elective surgeries have cancelled on Tuesday.
Brendan Lawlor of the HSE asked that people only visit hospital emergency departments and GPS "if it is really necessary".
The three victims were killed in separate counties following tragic incidents directly linked to the strongest storm to strike Ireland in more than 50 years.
The public's adherence to warnings to remain indoors is credited with preventing further loss of life during the storm.
Trees that were hundreds of years old slammed onto roadways while everyday objects became projectile missiles in the Hurricane force gusts.
The first fatality occurred at approximately 11.40am outside Aglish village, Co Waterford.
Clare O’Neill (58) died after the car she was driving was struck by a tree. She was due to celebrate her 59th birthday on Tuesday October 17.
Ms O’Neill’s mother, who is in her 70s, was a passenger in the car and was injured during the incident and was transferred to Waterford Regional Hospital.
Her injuries have been described as non-life threatening.
Clare O’Neill worked as an oncology nurse for over three decades and recently worked as Cancer Support Co-Ordinator with the Cork ARC Cancer Support House.
“She was a very jolly woman, very helpful,” local shopkeeper Richard Hurley said.
“It’s a big shock, it’s a miserable morning, a young woman like that (dying) in such a tragic accident.”
The second tragic death caused by Ophelia occurred at around 12.30pm in Cahir, Co Tipperary.
Local man Michael Pyke (31) was attempting to clear a fallen tree with a chainsaw when the tragedy occurred. Gardai believe that Mr Pyke was attempting to move the tree on the Cahir to Ardfinnan road, when another tree collapsed and struck him.
Emergency services were called but Mr Pyke was pronounced dead at the scene. His body was later removed to Clonmel Hospital.
Meanwhile, at approximately 2.45pm a serious road traffic collision occurred in the Ravensdale area of Dundalk, Co Louth. Fintan Goss, who was aged in his 30s, was the driver of a vehicle when it was struck by a tree. It is believed the married father-of-two had been travelling home early from work due to the storm when tragedy struck.
Mr Goss lived in Ravensdale with his wife and children.
They were supporters of Fine Gael and last night the chairperson of Dundalk Municipal District, Cllr John McGahon (FG) said: “This is an absolute tragedy. Fintan and the Goss family are extremely well regarded in the community.
“He will be greatly missed by his friends, family and the local community in Ravensdale. Our thoughts are with his family at this terrible time.”
Taoiseach Leo Varadkar extended his sympathies to the families of those killed.
President Michael D Higgins also extended his sympathies to the families who lost loved ones during hurricane Ophelia.
Speaking as he continued his State Visit of Australia President Higgins said; "My heart goes out those who have lost loved ones and what they must be suffering".
The President also acknowledged that the extent of the destruction the storm caused will continue to emerge today.
"Some people will have been badly affected by flooding, others will have to reconstruct houses," he said. "I hope that once again that people will come to gather in a spirit of cooperation."
Taoiseach Leo Varadkar has said that the "full resources of the state" will be deployed for the clean-up action.
"The full resources of the state will be deployed for the clean up operation. Crews from UK and Northern Ireland will be in to help," he told RTE.
This follows a call from British Prime Minister Teresa May yesterday when she offered the Taoiseach assistance in the recovery effort.
Mr Varadkar also urged continued continued caution today.
"We have had three tragic deaths but the most important thing is that no-one else else losses their life. There are still dangers even if the storm is gone.
Schools will reopen this morning, and school buses will be running, unless they have safety concerns, the Department of Education has confirmed.
The final decision on whether a school reopens will come down to whether there are any safety issues arising from Storm Ophelia.
In a statement yesterday, the Department said “schools must ensure the safety of those in their care and give due consideration to this when making a decision to re-open.”
The Department also advised that if a non-State owned school needs repairs it should, in the first instance, contact its insurance providers, before seeking any emergency funding from the State.
For any State-owned buildings, school authorities are free to apply for funding under the Department of Education’s Emergency Works Scheme.
Education Minister Richard Bruton thanked principals, teachers, students and parents for their co-operation with safety measures over the past two days.
Around 10,000 people whose hospital outpatient appointments were cancelled due to Hurricane Ophelia on Monday may have to wait weeks to get a re-scheduled date.
The cancellations, which were called for safety reasons to prevent public patients having to make journeys in hazardous conditions, could result in extra clinics being laid on in some cases to help clear the backlog, Damien McCallion, the HSE's national director of emergency management, said yesterday.
He said other patients who had appointments with mental health and other services will have to be re-scheduled.
Health services continued to face disruption yesterday, although all outpatient clinics went ahead.
Some waiting list patients awaiting planned surgery had their operations put back because of a lack of beds.
Hospitals were under pressure to free up beds that were occupied by patients who could not be discharged due to the storm.
Mr McCallion said some hospitals opened closed beds and this helped to relieve overcrowding in hospital A&E departments.
The emergency departments were busy in the afternoon as patients, who held off seeking medical care on Monday, attended services yesterday.
Ambulance services in some areas of the country faced difficulties due to fallen trees and road blockages caused by the storm. This led to delays in some cases.
Mr McCallion said homecare services were also disrupted and some patients who needed medical equipment that was powered by electricity had to be moved to community hospitals after electricity supplies were affected.
In the run up to the storm, home care and other staff had tried to visit as many people as possible who rely on home visits in counties which were on "red" alert.
Five hospitals were in areas that suffered electricity blackouts and had to revert to their generators.
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League of Ireland
The FAI have confirmed that Cork City's fixture with Derry City will go ahead on Tuesday night at Turners Cross despite the damage done to the stadium during Storm Ophelia today.
Concerns have been raised after a number of photos and videos emerged online showing people swimming in rough seas and walking along piers during the worst storm to hit the country in half a century.