If some cataclysm happened, the atomic theory (hypothesis, truth, fact, etc.) of matter would help the survivors better than any other bit of truth.

All things are made of atoms - little particles that move around in perpetual motion, attracting each other when the are a little distance apart, but repelling upon being squeezed into one another.

From that you can, with a little imagination, surmise (and be mostly correct) many things. Especially if you remember that the atoms are always in motion (except at absolute zero, but we've never been that cold, and that's the definition of absolute zero, but there's an exception there, too: helium).

Use water as an example. Moles are atoms stuck together in discreet units.

Define the jiggling motion of atoms (and molecules) as heat. Increasing the motion of the particles increases the temperature of the water (because temperature is a measure of the heat in the water). Or the opposite way, increasing the temperature increases the motion, increases the space between molecules. Eventually some molecules will have enough energy to escape the attraction to other molecules (bond, pull between molecules), and break away, becoming vapor instead of solid or liquid.

Continuing with water example, steam vapor molecules produce an average push, known as pressure, against our gross senses. The effort required to counteract this average push from the molecules is the pressure (well, pressure times area is the force, but that's in parentheses).

From the pressure definition, you get increasing the area but keeping the number of particles the same, descreases the number of collisions, so drops the pressure. Double the number of particles with the same speed (i.e. same temperature) would double the number of collisions, so you know that pressure is proportional to density.

Increasing the temperature without changing the density of the gas, however, increases the number of collisions, so you know that increasing the temperature increases the pressure, too.

Using a piston, you can compress the piston, which gives the molecules less room to move, which will increase the number of collisions on the surfaces. So, compressing a gas slowly will increase the temperature, while decompressing a gas will lower the temperature.

Solids are materials with a definite place for every atom. Repeative patterns are crystalline arrays. Ice forms with a hexagonal(ish) pattern that leaves holes in the structure, which is why ice has a greater volume than water.

Melting is the process of increasing the motion of the solid's molecules so that they shake out of place.

Helium's special. Even at absolute zero, the molecules still have energy enough to move. Need to apply great pressure to stop helium's molecules.