From entrance to entrance 25 minutes.
Yes - the Northern Line (Charing Cross Branch)
Taxi is quickest and most expensive. Tube is cheapest but the journey is more complicated (you have to change lines).
Yes, you can use the northern line.
Westminster or Waterloo
Take the Piccadilly line from Heathrow to King's Cross St Pancras (St Pancras is the Eurostar station).
The nearest tube station is Waterloo.
It's cheaper and quicker to go by tube
From Waterloo take the Bakerloo line to Oxford Circus. There transfer to the Victoria line to St. Pancras International rail station. Journey takes about 20 minutes with one change of train. Check the 'London Tube' site for service delays and restrictions.
Waterloo??
Central, Circle, District, Metropolitan, Waterloo.
The Courauld Institute of Art is located in London at Somerset House, Strand, London UK. It is close to the Covent Garden and Waterloo Bridge. It can be accessed on the tube at Temple, Charing Cross and Waterloo.
Waterloo and Westminster are both very close to the London Eye. Waterloo is on the Jubilee Line, Northern Line and Bakerloo Line. Westminster is on the Jubilee Line, District Line and Circle Line.