Friction on atomic scale I am getting into friction on an atomic scale. For instance, take two rigid layers of atoms of the kind A that are placed on top of each other, just like putting two boards of wood on top of each other. Then place some atoms or molecules of the kind B between those two rigid layers, i.e. put some pebbles between the two wooden boards. Now start pushing one of the rigid layers horizontally, i.e. start pushing the wooden board on top.
On the macroscopic scale, we will be able to treat this system with Newtonian Mechanics and (relatively) simple approximations, i.e. friction forces.
How about the microscopic scale? When I google "friction microscopic scale", I get lots of results about ongoing research that is a bit above my level.
Where would be a good place to start reading about this in general?
I plan to dive into this, bearing in mind to maybe go on and model such systems computationally. 
 A: At the microscopic level the source of friction is the force between the atoms/molecules in your system.
For example, if you remove your $B$ layer then when you bring your two layers of $A$ together they will simply bond just like two crystal planes do in a chunk of solid $A$. To find out what effect the layer of $B$ has you'll have to calculate the interatomic forces between the $A$ and $B$ layers.
About 15-20 years ago I got a postdoc to attempt these calculations for a surfactant layer adsorbed on the surfaces, but it turned out to be impossible to do the calculation with any useful level of physical realism. Obviously computers and computational techniques have a got a lot better since, but I still think an ab initio calculation is still likely to be demanding.
In friction between macroscopic objects you are not sliding the contact layers over each other but rather fracturing the contact patch. When you touch two macroscopic surfaces together the asperities (high spots) touch and the surfaces cold weld at these contact points (the article I've linked has a good illustration of this). As you slide the surfaces the asperities deform then fracture apart. The friction is mainly due to the energy required for the fracture. So really you need to calculate the potential between the two surfaces.
There must be lots of literature on this problem so it would be worth a search of the current literature - my knowledge of it is (at least) 15 years old!
A: There are two famous models to deal with atomic-scale friction. One of them is Frenkel-Kontarova model, the other is Prandtl-Tomlinson model. Prandtl and Tomlinson's model is much more useful and famous. In order to get a fundamental knowledge about it, I can recommend this paper: https://journals.aps.org/prb/pdf/10.1103/PhysRevB.55.2606. 
