The BBC transport reporter Tom Symonds looks at the two arguments.

This will be the week that decides the future of London's crucial underground system.

The 1.5 million passengers a day who use it have become used to regular breakdowns.

The government believes by bringing in engineering companies to rebuild tracks and tunnels, it can guarantee �4,000 of investment for every household in London.

But Ken Livingstone has bitterly criticised the plan, calling it an "underground version of Railtrack" and a potential safety risk.

Private companies

There have been more than seven months of manoeuvring and confrontation between the two sides - but an agreement has proved impossible.

Mr Livingstone's Transport Commissioner, Bob Kiley, was made Chairman of London Transport and given permission by the government to try and renegotiate the public-private partnership (PPP) contracts to give him day-to-day control over the private companies.

He and the mayor believe that unless they can order the contractors to carry out specific work on the line at short notice, services will suffer.

But Mr Kiley has failed to reach an agreement with the bidders.

Last chance

On Tuesday he was sacked from his role as chairman of London Regional Transport by Transport Secretary, Stephen Byers.

Monday's High Court hearing is Mr Livingstone's last chance to stop the public-private partnership.

The legal challenge is based on the claim that doing a deal with the private sector would prevent the mayor developing his own policy for "safe, economic, integrated and efficient" transport under the terms of the legislation that set up his office.

Ministers are confident they will beat the challenge.

There will be no witnesses as such.

Win over

Instead, Monday will be spent getting to grips with the written evidence.

Starting Tuesday, the two sides will begin to make submissions in an attempt to win over the judge, Mr Justice Sullivan.

A decision could come as early as this Friday.

If it goes against the government, ministers may have to rethink their whole approach to delivering a better Tube system, on which London can rely.

If they win, it is possible the contracts for the public-private partnership will be finalised and signed quickly.