The most important for advanced research is the mathematics archive. It contains more or less all (important )mathematical (and physics) research papers since 1990.

This makes it easy to find up-to-date information at no cost, in contrast to the situation in some other sciences. This is historically a new situation, meaning that a young researcher does not need access to a hideously expensive library---just a computer with a not too slow internet connection.

The only, but it is big, problem is that research papers are highly technical and you have to know what to search for. But for example, if you want to find a recent paper by a certain author, which you have seen as a reference in another paper or book, it is a good idea to search for it on the archive (or the home page of the author), instead of trying to find a way of accessing the journal in which it was published. Or you might want to see what further papers that author has written.

The archive, however, contains few books(even though there is an increasing number of lecture notes). Some thousands of such can be found through the links at the following site.

Books on line

Again, it will take some time to distinguish between the very advanced and beginners texts, but both are available there for several lifetimes reading. Best is to get advice on what to read from someone.

Information about the math community---for example presentations of the recent Fields medal winners--- and a lot of other things might be found at the homepage of the american and european mathematical societies

American and European mathematical society.

(But if you want to understand better why one of the Fields medalists declined the medal and probably also will say no to the prize of $ one million he would get from the

Clay institute

for solving Poincare's conjecture, you will have to google. )

There are many forums for internet math discussions at all levels at Drexel University .

In particular there is one for math research , and it is possible to post questions there and sometimes get answers, or pointers to relevant books or papers. Mathforum

Finally, there is a special site for mathematical resources for Africa:

"e-Math for Africa"

where there are links to many journals, and also tips for how to get access to information that is not free, like the second big research tool (in addition to the archive): the mathematical reviews (Well, you have to find a sponsor university in Europe or US...).

Math reviews is a journal that contains short descriptions of almost all mathematical papers ever written...