Auch, indeed... You're right.
Will this work then, if I do port-forwarding?
You can forward all the ports you want on your router, but if you are sitting behind a NAT (from your ISP) there isn't much you can do. Google for more info, but basically ISPs implemented NATs because the internet was running out of IP addresses. The advantage to a NAT is that your ISP can group a whole bunch of customers behind a single public IP address. The disadvantage as you are experiencing is that you have no way to allow incoming connections (how is the NAT supposed to know which customer the intended data was for?).
In essence, your own home router is a NAT because it hides all of your other devices you have connected to it behind a single connection to the internet (through the ISP's modem). That is where port forwarding comes in, when you setup port forwarding the NAT (your router) now knows where to send incoming data for a specific port instead of just dropping it.
Generally ISPs offer a more expensive 'business' plan that includes a static public IP address which would then allow you to handling incoming connections (port forwarding) and host your own server.