How to show the local and the router IP?

You can get the list of local IP addresses very easily:

System.Net.IPAddress[] localIPs = System.Net.Dns.GetHostAddresses(System.Net.Dns.GetHostName());

Unfortunately, it may not be possible to get the IP address of your router. You can get the IP address of your default gateway, which MAY be your router, with this:

ManagementObjectCollection nacs = new ManagementClass("Win32_NetworkAdapterConfiguration").GetInstances();
foreach (ManagementObject nac in nacs)
    {
    if ((bool) nac["ipEnabled"])
        {
        string[] gateways = (string[]) nac["DefaultIPGateway"];
        foreach (string sGate in gateways)
            {
            Console.WriteLine(sGate);
            }
        }
    }

However, it isn't guaranteed that this is your router: All my PCs sits on a Gigabit switch which connects to a 100Mbit ADSL router. The switch doesn't have a separate IP address, since it's IP's are handled by the router.

use is code:

using System.Net;

namespace wfamyip
{
    public partial class myip : Form
    {
        public myip()
        {
            InitializeComponent();
        }
        private void btnip_Click(object sender, EventArgs e)
        {
            String strHostName = Dns.GetHostName();
            IPHostEntry ipEntry = Dns.GetHostByName(strHostName);
            IPAddress[] addr = ipEntry.AddressList;
            foreach (IPAddress add in addr)
            {
                lblip.Text = add.ToString();
                //MessageBox.Show("IP Address {0}:{1} ::  " + add.ToString());
            }
        }

    }
}

Good luck