My blogfriend since the very beginning Hootin Anni had always helped Bloggers when they were stuck with something or if she had discovered something new.
This time she helped me out with a replacement for Google Reader. It is called "Feedly" and works with Mozilla Firefox. As I only work with Mozilla Firefox since Internet Explorer doesn't like Blogger and takes ages to load a page, this tip was just what I needed.
I downloaded "Feedly" which is very easy and it installs itself on the Mozilla Firefox startpage :

See the little green sign ? Just click on it. Feedly imports all your friends from Google Reader

and you arrive on a perfect follow up page for your blog. It is even more clear and detailed ! Here I clicked on "Today"

and here on "Latest" you see it looks quiet like Google Reader.
Thanks to Anni my problem was solved and I just can follow new posts as usual. Maybe you should inform your friends who will have the same problem when Google Reader disappears.