sort and sum costs by month and by type

Hello everyone,

I have 1000+ items expense list across 15 different cost types and all different payment dates. I need to show a monthly sum of the different cost types. I have a feeling that it is an index/match formula but I always end up getting confused with that. I also don't know if it is possible to sum expenses in a month as I have specific dates in the cells. Please find attached a simplified version of the expense list (well, let's hope I can actually attach it).
I am so grateful for all you geniuses in advance.

Many thanks in advance