Internal circuitry of integrated circuits
I mean, do IC manufacturers publish these? 


Usually, they don't. It's their business secret, on which the existence of the company depends.

You'll find some open chip designs, especially in the academic environment. But it's really the exception.

Also, aside from people who just want to produce the same IC, these would rarely be extremely useful – you need to know a lot to understand what's going on there at the individual standard cell level (digital logic) or the analog primitve level (analog), and for more complex chips: what use would it be if, after looking at it, you knew the function of every of the billions of gates? Still not giving you any "big picture".

For a few very old (think: 30 years and older), very simple, analog chips, some manufacturers print the top metal layer in their datasheet – Maxim does that. It's not really giving you any insight about what the chip does without the rest of the description, but it allows you to understand how the chip's components have been arranged. It's neat, but I don't know anyone who's ever been able to do a better engineering job because of having that.


  Is it possible to know the internal circuitry of integrated circuits


Of course, whoever designed the ICs knows that – if we're talking digital logic, these are typically designed using Hardware Definition Languages, which abstract the electronics, and converted to a mask image through software.

So, in a partnership with one of these companies, you might get access to that source code (it's usually something they'd be very careful about not giving away).

One can reverse-engineer many types of ICs (that's a lot of effort that requires extremely nasty chemicals, a lot of experience it seems, and very expensive equipment – won't get far without an raster electron microscope on somewhat modern chips. Think of costs > 6·10⁵ € for a microscope that can "see" gates of a 45 nm process. And that's an old process.).

The problem, again, is that in digital logic, the reverse-engineering of single cells doesn't give you what the device does in total, so you need to get very good about automating understanding of microscopic pictures and piecing them together automatically. For analog, well, there's many aspects of the silicon production process which you can't "see" in the end product easily, but which define the function of things, so, you could usually get a rough understanding of "what happens", but rarely something good enough to e.g. simulate the circuit.