Hi, at home, i have two PC´s which are connected to a router. this router provides the internet connection. Now i habe a server on my local machine #1. And the client is on another remote machine at work. I have three IP adresses. One for the service provider, one for the router, and one for the local machine. How can i make it possible to send network packets to the local machine at home from the remote machine at work? thanks in advance Gammastrahler

You need to forward the appropriate port(s) on your router. Usually you connect to your routers IP address (often 192.168.0.1 or something) with a web browser, from within your local network, and look for a port forwarding option.
You'll want to forward the port (e.g. 1234) to the IP address of the machine the server is on (e.g. 192.168.0.2).
Apart from that, there's no way to bypass the router using TCP/IP. If you're using UDP, you can use hplus0603's NAT punch through method.

Actually, IF you have a publicly visible IP address for the home server, AND your router is smart enough (most home routers aren't), THEN you can set up a static route from the router to the home server's address. This also assumes that your ISP is smart enough to route both addresses to your incoming router.

An alternative is to put the server machine as a peer with the router, by making your DSL/Cable modem connect to a switch. This works no matter what the router (assuming you got two IP addresses from your ISP).

Some routers also allow you to configure a DMZ machine, which will get all traffic that comes in at the router's IP address, if it's not return traffic from a NAT-ed connection. If you have DMZ support, then forward your router's IP to the internally placed server; no second IP needed.

In either case, make sure you have a good firewall and tight policies for the publicly visible server.