@Edvin,
I don't know if I am supposed to link to other sites in this forum, but the following website is a good summary of Kant's Prolegomena, and it explains a priori, a posteriori, synthetic and analytic well.
Kant: Judgments
Also, I tried to explain how Kant can come to synthetic a priori judgements in a post in the Kant area of this forum. I would try again, but time is limited.
I enjoy dicussing Kant, a lot. Hopefully we'll be able to have some profitable conversations together.