In the USA, as far as I know, the main grants available to mathematicians are collected on the NSF or the AMS websites [please, correct me if this perception is inaccurate]. On the other hand, for European countries for example, the situation seems to be much more scattered. In addition to the various ERC grants, I would like to use this post to collect other specific funding programs that mathematicians may apply to (at the national or international level).
In fact, we could make the question more general and ask it on a world-wide level: What funding programs are available supporting mathematical research and researchers? It would be nice to make this question community-wiki and possibly have an answer addressing each country in the world and one for multi/inter-national funding programs.
This question appeared in Academia SE specifically for Italy, but I think it's very relevant in this generalized form for the MathOverflow community.