The nature of the space in which we exist I'm looking for pointers to give me a better understanding as to what 'space' is.  I do not mean the descriptions of what's in 'space' i.e. not interested in descriptions of outer space filled with particles and quantum foam.  I'm interested in learning more about what the 3D 'shape' is actually made from, so for more explanation, if before the big bang there was nothingness and now after the big bang there is something (in my language a 'space') what is it made of.  Is it granular? Is it an agglomeration of grains at the Planck length?  Presumably, if 'space' is expanding then more of it is being produced 'from outside' (Branes?). If not, then again presumably 'space' is being stretched and its 'shape' is changing. I don't even know the name of this subject/topic but I'd love to know who is writing on it and learn more. Thanks for reading, hope you can help.
 A: Our best current effort at addressing a question like this is through a combination of quantum field theory and general relativity. Quantum field theory describes a linked collection of interacting fields called quark field, colour field, Dirac (electron/positron) field, electromagnetic field and some others. The electromagnetic and weak fields are two parts of a single more complex field, and it is suspected that all these fields are aspects of one more complex thing. My answer to the question "what is space?" is "it is this set of fields."
But what is a quantum field? It is a physical structure that extends everywhere (making the 'fabric' of space) and has properties encoded in the way it interacts with other fields and with itself. This is quite a subtle structure however. It respects relativity principles in such a way that you can't tell if you are moving relative to it---that type of concept does not apply. When these fields are in one state then we say there is matter present; when they are in another state we say there is no matter present. But the fields are present in either case. So the vacuum of space, which is what you are asking about, is essentially this collection of fields and it thus has a rich number of precise properties and relationships.
General relativity now comes along and tells us that when you look on larger scales there is quite a lot of subtlety about how space in one region relates to space in another region. This is where we start to talk about geometric ideas such as "curvature" of space, and the idea that space is expanding. The term "curvature" is a reference to the fact that if one studies geometric things such as triangles made of solid objects, as described by the quantum fields, then you get laws of geometry which are like the laws applying to geometric lines drawn on a curved surface.
As to whether space is granular, we don't really know for sure, but the evidence is that it is not granular in any simple sense. However quantum physics allows for intermediate cases which are neither completely smooth nor granular either. There are various theoretical efforts to try to understand this. $M$-theory, or string theory, tends to look more smooth. Loop quantum gravity tends to look more granular, but this is a very rough way of putting it.
When space expands then you are correct that more of it is being "produced" and there are some deep puzzles associated with this,
associated with observations which suggest the expansion is accelerating. But people working in this area will tell you that it does not always give the impression that more space is more "of" anything. It sort of is, and sort of is not. I think we just don't have a very clear or final understanding here. But maybe others will come to a different judgement.
A: Andrew Steane, thank you for taking the time to respond and also for the clarity of your description.  If I can play back what I think I've understood from your explanation could you please confirm or correct as approriate.
Empty space isn't as empty as it seems, at every point there is a collection of fields that take some value or another (or a distribution of values), so from your examples magnetism, the nuclear forces, gravity, electrons, protons etc. are all carried by those fields.
These fields are what the world and our universe is made of.
My question concerned the nature of the 'empty space' itself (I had considered it to be a seperate entity) i.e. was it structually different to those forces that resided within it, effectively could 'space' be considered to be 'just' another field.
If so would the vibrations in this field manifest particles that would give rise to an emergent 'space' i.e. some granular quantized structure.
My intuition was that the answer may have been 'yes' but from your reply this is in fact erroneous.
So if I can please take as a starting point your view that there is no 'space' field and that 'space' is (presumably) just a construct created by the human mind and that in actuality it is a manifestation of the collection of the above mentioned fields.
Are you're saying that in your view 'space' is an illusion?  If so then this implies that the mathematics of field theory, which must embed some notion of 3D structure in order to assign a value to each 'point', renders 'space' to be just a mathematical expedient?
Do I understand correctly that your view would be that the human mind therefore constructs x, y and z coordinates to rationalize and compute it's everyday experiences of movement and position?
You mention Loop Quantum Gravity as investigating the granularity of structure, what then would be the unit of granularity?  Presumably some agglomeration of the individual field values at some constructed mathematical reference point?
A: 
I do not mean the descriptions of what's in 'space' i.e. not interested in descriptions of outer space filled with particles and quantum foam.

In that case you are not asking about the (quantum) fields that are in the space, but the geometry of the space itself. Currently the best description of the space in that sense is given by General Relativity.
First, one should mention that the space is inseparably combined with time into something called the spacetime. This is not only true in General Relativity (where spacetime can be curved) but also in Special Relativity (where spacetime is flat). Time is inseparable from space similar to the way e.g. one dimension of 3-dimensional space is inseparable from the other two.

I'm interested in learning more about what the 3D 'shape' is actually made from, so for more explanation, if before the big bang there was nothingness and now after the big bang there is something (in my language a 'space') what is it made of. Is it granular? Is it an agglomeration of grains at the Planck length.

Now this is the area in which there are no definitive answers known yet, although there are some great efforts being made to find better understanding. Also in this area the nature of space(time) could be (more inseparably) linked to the nature of stuff inside it. In the first part, what are you looking was General Relativity (which is well-defined and well-understood by itself) and in this part what are you looking for is (probably) Quantum Gravity - a combination of General Relativity and Quantum Field Theory, which is not yet formulated and there are many proposals on how to try to formulate it.

Presumably if 'space' is expanding then more of it is being produce 'from outside' (Branes?). If not then again presumably 'space' is being stretched and its 'shape' is changing.

The way space(time) changes is that distances (described by something called metric tensor) inside of it change. It could be naively described as space stretching itself, but, unlike regular stretching of elastic materials, the spacetime does not have any information of the "amount of stretch". Also, there is no such thing as "amount of space", i.e. there is no space being created or destroyed (although the capacity of space (i.e. volume) in the space can change - it changes when the distances change). What spacetime can have is curvature and General Relativity governs its dynamics.

I don't even know the name of this subject/topic but I'd love to know who is writing on it and learn more. Thanks for reading, hope you can help.

First name of the topic is General Relativity, which describes gravity as a curvature of the spacetime. Later, for attempts to unify it with Quantum Field Theory, the name is Quantum Gravity, but that is way more advanced and with almost no definitive answers yet. Hope this helps. :)
A: In this article ("What is space made of? It's complicated ...") it is written:

Douglas Adams was right. And not only is space big, but we also don't know what it's made of.
Astronomers have worked out that only about 5 percent of our universe consists of baryons — the particles which make up atoms, which in turn make up molecules, which in turn make up everything we see, touch, smell, and taste.

So don't expect an answer.
I can look at your question though and try to answer it in that context.
Atoms of space (grains, as you call them) appear only in a quantum theory of gravity, where the atoms are the quanta of space. No such theory has been found yet (after many decades). I doubt if such a theory ever can be found because I doubt gravity can be quantized.
I read in a previous answer:

But what is a quantum field? It is a physical structure that extends everywhere (making the 'fabric' of space)

I don't think the physical structure of a field "makes" the fabric of space. It is the fields that need space. Space is seen as continuous. Only in the case of a quantized gravity field, space becomes granular. But such a theory doesn't exist and as I already said I think gravity can't be quantized (decades of trying and not succeeding gives at least some back up for my conjecture).

Is it an agglomeration of grains at the Planck length?

No, if quantum gravity is true, you cant envision space as built up from basic units (like building a wall from bricks). It's not that simple. You can't build up space out of Planck-sized cubes. That would be very easy! You can find more about the building up of space from Planck-sized volumes in the Loop Quantum Gravity (LQG) approach, another attempt to unify QM and GR.

Presumably, if 'space' is expanding then more of it is being produced 'from outside' (branes?)

I'm not sure what you mean by stating that in an expanding space than more Planck volumes (space atoms) are imported from branes. I'm not a fan of string theory but I think you mean those space atoms are extracted from the collection of the space atoms residing in the branes. I think string theory doesn't incorporate space atoms. It incorporates gravitons though, which obviously aren't space atoms.
The AdS/CFT correspondence embodies (in a very concise way) the hypothesis that a 4d Anti-de Sitter Space on which boundary exists a Conformal Field Theory (a color field with a huge number of different colors) gives rise to a gravity field inside the boundary. This is not of real importance to your question, but nevertheless. As I said, in string theory, no atoms of space exist.

If not, then again presumably 'space' is being stretched and its 'shape' is changing.

Why and how should its shape (of space) be changing? Maybe the Planck-length volumes just grow in size if more space appears.
The final answer:
Presently, we don't know the Nature of space (time has to be included too, and atoms of space imply atoms of time; see this article. If space were granular then the light of different frequencies would have to reach us at different times, which hasn't been observed yet). It's my guess though that spacetime is continuous up to the smallest scale, the Planck scale.
