The Greek philosopher Democritus, who lived between 460 and 370 BC, thought that matter was composed of tiny, indivisible objects in perpetual motion. He called these theoretical objects "atoms" - from the Greek word "atomos", meaning something that could not be cut.
In Democritus' time, there was no way to verify this idea experimentally. However, by the nineteenth century work in chemistry and physics showed that matter does have a structure invisible to the human eye.
The basic constituent of that structure is the atom. It is the basic building block of every element.
Every element, from hydrogen to uranium and beyond, has its own unique atom. Atoms give the elements their physical and chemical properties, depending on their own inner structure. Atoms can join to atoms of other elements to form molecules (such as water molecules) if they react appropriately with the other element's atoms.
But they are not fundamental building blocks and Democritus and others who held the atom to be the fundamental particle were wrong, as experimental work in the first half of the twentieth century proved. They are instead built of smaller particles - electrons, neutrons and protons. Atoms consist of two parts: a nucleus, which is a mass of protons and neutrons, and an orbiting set of electrons. Most of an atom is in fact empty space between the orbiting electrons and the central nucleus.
Electrons are tiny, very low mass particles with a negative electric charge. The simplest atom, hydrogen, consists of one electron orbiting one proton (more of these later). Hydrogen gas is the main constituent of stars and is the most abundant element in the universe. Other elements have more electrons and more of the other particles too. Electrons whizz round the nucleus of an atom in a cloud. When the atom reacts with another atom from a different element, electrons are exchanged and the two atoms join through this process. These reactions are what we observe when things burn, and when new substances are formed, such as water or carbon dioxide.
Why does the cloud of electrons orbit the nucleus? The nucleus is made up of two types of particle, both much more massive than the electron: protons, which are positively charged, and neutrons, which have no charge. In most stable atoms, the number of protons equals the number of electrons (but there are exceptions to this rule, called ions, which are different forms of elements). Protons and neutrons bind together to form the nucleus (often, but not always, in equal numbers). Because protons are positively charged, the attraction between them and the electrons creates the energy that keeps the electrons orbiting the nucleus. The number of protons in a nucleus determines an atom's atomic number.
But why should protons and neutrons bind together in this way? Protons and neutrons themselves are not fundamental particles. They are both composed of three smaller particles, known as quarks. There are several different types of quark, which is why the proton has charge and the neutron does not: they are made from different types of quark. Quarks bind together through the fundamental force known as the strong nuclear force - and this interaction between the quarks of protons and neutrons holds the nucleus of an atom together.
It is the nucleus that is involved in nuclear reactions, what is sometimes known as "splitting the atom" and is the basis of all nuclear weapons, as well as being the Sun's source of energy. Nuclear fission, the basis of the atomic bombs that were dropped on Japan in 1945, involves bombarding a uranium or plutonium atom with a slow moving neutron. The atom splits into smaller atoms, releasing a huge amount of energy in the process. Nuclear fusion, the reaction taking place constantly at the heart of the Sun, involves two light atoms crashing together and fusing to form a heavier element, releasing vast amounts of energy. In the Sun's case, hydrogen atoms under great pressure and therefore moving very quickly fuse to make helium and lots of light and heat.
The nuclei of atoms are also involved in radiation. In the process known as radioactive decay, unstable atoms such as some forms of uranium, or radium, spontaneously release particles from their nuclei and so "decay" to a lighter and more stable element. These particles, such as alpha radiation, which is a block of two protons and two neutrons, can either be relatively harmless or dangerous to living things, such as beta radiation - emission of fast-moving electrons (although it is relatively easily stopped).
As far as we know, electrons are fundamental particles and have no internal structure.
Is that it? Is that the definitive truth of atoms?
Not quite. The quarks that make up protons and neutrons in the nucleus of an atom are bound by a force, but this force is mediated by particles. Particles which carry force are known as bosons (as opposed to fermions, which are particles that make up matter). So inside the nucleus of an atom, there are gluons, carrying the strong force, and in some atoms there will be W and Z bosons, which carry the weak force.
The inside of an atom is not a static place - it is a constantly moving hub of quantum activity, where particles inside particles and particles between particles are, together, always keeping the atom in existence.
And beyond that?
There is a theory known as string theory, which is widely discussed and worked on by physicists around the world, though it has no experimental basis at this time. String theory posits that all these particles are the results of vibrations of immeasurably tiny strings - one dimensional objects that exist either as lines or loops. The different types of string and the different quality of vibration gives rise to events that we have perceived as particles. String theory is an immensely detailed and complex branch of physics, widely regarded as possibly being the start of humanity's ultimate understanding of the universe.
Atoms are fascinating, complex objects. Over the past two hundred years we have delved further and further into them, uncovering incredible new science and powerful new technologies along the way. The challenge for modern science is twofold: to try and make use of nuclear fusion, in order to provide clean energy - a very expensive and so far largely unsuccessful process - and secondly to probe those tiny particles at the very heart of atoms, to see what more can be unearthed. That is more or less exactly what the Large Hadron Collider at Cern is trying to do.