Atoms are a small building blocks of matter, but not the smallest. Atoms are made up of electrons, protons, and neutrons.
Electrons are (as far as anyone has been able to tell) honest-to-god point particles, i.e. they have no further internal constituents (I'm not saying they don't have spin or that they can't be described by wave functions, etc., just that they are not made up of any sub-particles).
The situation with protons and neutrons is a bit trickier, but it basically suffices to say that they are made up of quarks and gluons, which are also point particles, in the same sense as electrons (as far as anyone knows).
So ... that's the BOTTOM. Let's work up from there...
Atoms can combine together (interacting via electromagnetic forces, the van der Waals force, etc.) to form molecules. Molecules are usually described in terms of atoms held together by covalent and atomic bonds.
Atoms can also combine together into large-scale lattices to form macroscopic solids, e.g. a chunk of copper is a bunch of copper atoms in held together electromagnetically in a lattice (up to domains, etc).
A textbook on chemistry can help elucidate further properties of molecules for you.
A textbook on solid state physics can help elucidate further properties of solids for you.
A textbook on the Standard Model of particle physics would be useful to catalog the known point-particles like electrons, muons, gluons, etc.
Finally, you mentioned "elements". By this, I believe you mean the different types of atoms, e.g., the element hydrogen, the element copper, etc. The different elemental atoms have different properties due to their differing number of protons, e.g. hydrogen has 1 proton, copper has 29 protons. In this matter, too, a textbook on chemistry will be useful to you.