Help with a formula!

Hi There

I have posted two images. Basically, I would like to log all of our expenses in our expense log (attached) and attribute them to a particular project. I would then like to have a sheet detailing project expenses, where it totals up all the expenses for a particular category and project in one cell (second attachment).

In words, I would like to have a function look up Project Z, and sum all cells from the expense log that relate to travel and add them up into the given cell on Project Analysis. And then do this for the others. I'm finding this very difficult to do! Does anyone have any solutions?! I'm new to all of this so any guidance, hints and/or tips gratefully received

With thanks