Question: I want to make a blinking light for my transformer when I charge anything with it. But as an educational exercise, I don't want to use any kind of IC. Can anyone help me?

Answer: 
You'd probably want a [astable multivibrator](https://en.wikipedia.org/wiki/Multivibrator). Here's one easily constructed with discrete components:

[![Transistor Multivibrator.svg](https://upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Transistor_Multivibrator.svg/1200px-Transistor_Multivibrator.svg.png)](https://commons.wikimedia.org/wiki/File:Transistor_Multivibrator.svg#/media/File:Transistor_Multivibrator.svg)  
By jjbeard - Own drawings, made in Inkscape 0.43, Public Domain, <https://commons.wikimedia.org/w/index.php?curid=873818>
How about an old-fashioned UJT?

[![enter image description here](https://i.stack.imgur.com/kqkLT.png)](https://i.stack.imgur.com/kqkLT.png)