Studying mathematics in Japan as a foreign student...
This page will be improved in the future (if you are a current or former student in Japan, please send suggestions to firstname.lastname@example.org), but meanwhile here are some very brief guidelines, which are aimed at potential graduate students (applying for courses leading to the degrees of MS, MSc, PhD etc).
WHERE TO BEGIN
It is essential to make personal contact with a potential adviser/supervisor at a Japanese university before you start applying for scholarships etc. A good way to do this is to ask faculty/staff members of your current university whether they might have colleagues in Japan who can be contacted for this purpose.
Grants are available from the Japanese Government which provide all necessary expenses. These are awarded on a competitive basis within each country. Information is available from every Japanese Embassy, and also via your potential host in Japan.
Living costs in Japan have fallen in recent years; currently (May 2003) they are probably comparable with those in many European countries. It is still possible to find surprisingly expensive items, but also surprisingly inexpensive ones too!
Knowledge of English is usually sufficient for all official aspects of studying mathematics in Japan, but this depends to some extent on the university and the host, so it is essential to make enquiries in each case. All professional Japanese researchers in mathematics publish their work in English, and research seminars are frequently held in English. On the other hand, some knowledge of Japanese is very beneficial for daily life, and as a student you will have various opportunities to study Japanese at little or no cost.
The following link (from Kobe University) contains helpful advice:
How to apply for graduate study at Japanese universities