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Atoms consist of a nucleus with electrons whizzing around it. The nucleus itself consists of neutrons & protons (how many depends on the element concerned). You may be wondering what cheap & nasty Malaysian cars are doing in an atom - but these are a different type of proton. Unlike the similarly-named cars, these protons don't fall apart. The same is true of neutrons.
The next question is why don't the molecules that those atoms form fall apart?The answer to that question is valence and the covalent bond. You see, a valence isn't just something pretty at the top of a pair of living-room curtains. Oh no . It means something different to scientists. Valence is where the electrons of atoms form a social networky sort of thing. But I'll leave the explanation of the intricacies of that to someone who knows what they're talking about.
Hydrogen atoms hang together in pairs because of the very strong magnetic force generated by the single electron whizzing round (45T ?)
There are many kinds of bonds, not only the covalent bond. (I hope you don't ask me, or I should write here an entire chemistry book).
Thank You Eth,If I understand you correctly, you have wonderfully explained that a gluon is the adhesive which keeps an atom together . It's a lovely explanation, a wonderful statement and even I am able to comprehend it.
DocI think what you are talking about, Quarks Protons & Neutrons etc is relevant but i think you are going a bit to deep.I think the question being asked is more to do with the various types of atomic bonding , how atoms fuse together,how two atoms share electrons for example and then form molecules.
They Dont call Neil Mr Ambiguous for nothing. 
Proton is a make of car from Malaysia.
My favourite intra molecular force is the weak Hydrogen bond that enables me to wet my finger and pick up breadcrumbs