The Lib Dems also say they could generate £1bn from legalising and taxing cannabis.
And they are offering pledges to young people including bus passes and help to get on the housing ladder.
To pay for the measures, they would add 1p to income tax, restore corporation tax to 20%, scrap the married couples' tax allowance and lower the level at which inheritance tax kicks in.
The Lib Dems, who have long called for cannabis to be legalised, say they would tax the drug and also say the move would lead to money being saved in police enforcement.
On the economy, the party says it would balance day-to-day spending while reducing national debt as a proportion of GDP.
But there is no repeat of the pledge to abolish university tuition fees - the promise the party controversially abandoned when it entered coalition with the Conservatives in 2010.
In its manifesto, the party said the "fairer" system established by the coalition had led to record university application rates.
'Fight for the future'
The flagship pledge of a referendum on the terms of any Brexit deal is at the heart of the Lib Dems' offer to voters, with the party hoping to gather support from Remain-backing voters.
The party believes there is no deal that could be as good as continuing EU membership and would campaign to stay in, cancelling Brexit.
Lib Dem leader Tim Farron said Brexit represented "the biggest fight for the future of our country in a generation".
"The Liberal Democrats want you to have your choice over your future," he said.
"You should have your say on the Brexit deal in a referendum. And if you don't like the deal you should be able to reject it and choose to remain in Europe."
The party, which served in government with the Conservatives between 2010 and 2015, is hoping to bounce back from its disastrous showing two years ago, when it lost almost 50 seats and was left with just eight MPs. It has ruled out striking any coalition deals after next month's election.
It is also pledging to reinstate housing benefit for 18-21 year olds, axed by the government last month, which it says could affect as many as 18,000 people and potentially lead to increased levels of homelessness.
As part of its housing offer, it is promoting a scheme in which those renting a property will be able to build up equity with every monthly payment, which they will eventually be able to convert into full ownership after 30 years.
The plan was first mooted by the party back in 2015.
This time around, it envisages developers and housing associations building thousands of new homes underpinned by loans and guarantees from a new Housing and Infrastructure Development Bank.
The total capital investment in the initiative, part of the Lib Dems' plans to build 300,000 new homes a year will be £3bn by 2022.
The bus pass discount on single and return tickets would be available to all 16-21 year olds ordinarily resident in England, using the same mechanism as the National Concessionary Scheme for the over-60s.
The Lib Dems have already pledged to protect per-pupil funding in England, which will cost £7bn over five years. In the manifesto it is going further, saying it will extend free school meals to all primary schools and triple funding for the early years pupil premium, boosting it to £1,000.
The party has also sought to play down 10-year-old remarks by Mr Farron, reported in the Guardian, in which he reportedly said abortion was "wrong" and called for the law to be tightened.
Speaking to the Today programme, Lib Dem election spokesman Sir Ed Davey said Mr Farron had since changed his mind and made it clear he was pro-choice.
"We wouldn't change the law," he added.
The Conservatives have accused the Lib Dems of being willing to prop up Labour in a "coalition of chaos" and seeking to overturn last year's referendum result.
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