Get your private and public IP from the Linux terminal

Both for a real server, VPS or just your desktop is useful to know which IP address your Linux system is using , this can be easily seen with some command if you are directly connected to Internet via a modem or a public IP of your company, but sometimes you are behind a router, a device that forwards data packets between computer networks, creating an overlay internetwork. A router is connected to two or more data lines from different networks, and at home it’s used to ???share??? your ADSL that usually has 1 public IP among all your devices, that will get each a private IP. For example at my home I’ve an ADSL Wi-Fi router that I use to get Wi-Fi connection to my 3 PC, 1 smartphone and 1 tablet (android), a printer and my kindle, every device has a private IP , it’s called private because it’s not visible on the public network that can only ???see??? the IP of my Wi-Fi router, but now let’s see how to check your IP on your Linux computers.