Is there strong interaction between electrons? I am not familiar with quantum mechanics at all. But I remember when I was at high school, we learned that strong interaction keeps protons next to each other while they repel each other because of electrostatic force ($F=\large{\frac{kq_1q_2}{r^2}}$). I saw this answer by David Z. He has written "Electron-electron collisions happen at low energy all the time". I got curious to know how is it possible? Because according to the formula above, when $r\to 0$ , $F\to \infty$. Then I saw John Rennie's comment under the other answer of the same question that was saying "collision means any close interaction causing a significant exchange of momentum" and this makes sense.
But, my questions are:


*

*Is there strong interaction between electrons?

*If two electrons approach to each other so much (I don't know how!), do they join together?
 A: The strong interaction that keeps protons together is a different kind of force (the strong nuclear force) which does not affect electrons. Electrons don't feel the strong force. They only feel the electromagnetic force and the left-handed ones also feel the weak nuclear force, which converts electrons into neutrinos. As a result, even if two electrons collide at high energy they will not cling together. There is no other force that can take over as in the case of protons.
Instead, the energy exchange may be large enough to produce extra particles. In a sense this is what was done at LEP (Large Electron-Positron collider), accept that the collisions occur between electrons and anti-electrons (positrons), which would attract each other and can annihilate each other. 
The strong nuclear force is described by the theory of quantum chromodynamics (QCD). However, at low energies, such as where protons attracts each other, it is rather difficult to work with this theory because it is too nonlinear.
A: Strong interaction refers to a different sense of charge instead of electrostatic charge. At least that is to talk about the most direct use of that interaction. There are much, much weaker corrections that have that as an intermediate interaction (virtual quarks). The joining is Cooper Pairs in superconductors. Look that up to see how it is mediated.
A: The Strong Interaction is responsible for holding together the quark and anti-quark configurations that make up nucleons (aka protons and neutrons). This is due to the necesity to hold together potentially repulsive configurations of these quarks and anti-quarks. As soon as we move past a certain distance away from a nucleon (I forgot what the distance was, exactly), the Strong Nuclear Force falls off exponentially towards zero. So, to answer your question... I suppose, we can say that electrons don't experience the strong nuclear force because 


*

*They are leptons (spin- $1 \over 2$ particles that do not experience the strong nuclear force), and 

*They are not composed of quarks and anti-quarks.

