Top 20 universities in the world and some of the main fields they teach:

1. Massachusetts Institute of Technology (MIT): Engineering, science, mathematics, computer science, economics, management, architecture, design, urban planning, humanities, and social sciences.

2. University of Cambridge: Natural sciences, mathematics, engineering, humanities, and social sciences.

3. University of Oxford: Classics, law, modern languages, history, philosophy, economics, politics, geography, and theology.

4. Harvard University: Humanities, social sciences, physical sciences and engineering, and life sciences.

5. Stanford University: Engineering, computer science, economics, business, law, mathematics, science, and humanities.

6. Imperial College London: Engineering, medicine, science, management, and business.

7. ETH Zurich: Engineering, science, architecture, mathematics, business administration, economics, and natural sciences.

8. National University of Singapore (NUS): Engineering, medicine, science, business, social sciences, humanities, and arts.

9. UCL (University College London): Medicine, law, science, arts and humanities, engineering, business and management, social sciences, and education.

10. University of California, Berkeley (UCB): Engineering, natural sciences, social sciences, humanities, and art.

11. University of Chicago: Economics, mathematics, physics, history, philosophy, and literature.

12. University of Pennsylvania: Arts, business, education, engineering, law, medicine, natural sciences, social sciences, and urban planning.

13. Cornell University: Agriculture, architecture, arts and sciences, business, hotel administration, engineering, human ecology, law, management, medicine, and veterinary medicine.

14. University of Melbourne: Business, engineering, humanities and social sciences, medicine, veterinary science, and law.

15. California Institute of Technology (Caltech): Biological sciences, chemical and physical sciences, engineering, mathematics, and applied physics.

16. Yale University: Art and architecture, divinity, law, medicine, music, philosophy, political science, and public health.

17. Peking University: Engineering, medicine, law, sciences, humanities, and social sciences.

18. Princeton University: Engineering, humanities, natural sciences, social sciences, and public affairs.

19. University of New South Wales (UNSW Sydney): Engineering, business, law, medicine, arts, humanities, sciences, social sciences, and design.

20. University of Sydney: Arts, business, law, medicine, science, and engineering.

21. University of Toronto: Arts, business, engineering, law, medicine, music, sciences, social sciences, and education.