The research assessment exercise is carried out every five years to evaluate the quality of research in universities in the United Kingdom.
The universities which have submitted departments for assessment - and it is a voluntary process - will seek to gain a slice of £1bn in research funding, which rewards the most successful departments.
The ratings, which have been decided by panels of UK and international academics, run from the lowest grade 1 up to the highest grade 5*.
The 2001 assessment exercise has shown a considerable improvement on the last figures, from 1996, with the number of departments rated as of national or international excellence rising to 64% from the previous 43%.
But this year's figures also show that there are fewer departments and researchers being submitted for assessment, suggesting that universities are less willing to put forward research which they feel might not receive a high enough rating to earn funding.
Only grades 3b and above qualify for funding from this assessment exercise, with nothing for those scoring 1 and 2.
Not about teaching
As universities are not required to submit all departments or all research staff within departments, these are not like school league tables.
The point of the assessment is to identify and reward successful research, rather than to provide data for young people choosing a university - and these tables do not refer to the teaching or quality of courses studied by undergraduates.
But they do highlight the institutions which have departments with the highest quality research - and the university with the most 5* ratings is Cambridge, followed by Oxford and by University College London.
Specialist institutions which have only a limited number of departments to submit for assessment will appear to perform less well in a simple ranking of totals of top grades - and institutions such as the London School of Economics appear to be stronger when the measurement takes into account top scoring departments as a proportion of those submitted.
In the BBC News Online tables, the assessment results can be searched by university or by subject area, where universities are ranked within each subject, from the top 5* down to 1.
Bear in mind that the listing does not include those universities which chose not to be assessed.