A fundamental particle is one that as far as we know cannot be broken down into smaller particles. At A level we are often taught that all matter is composed of the fundamental particles protons, neutrons and electrons. However this theory cannot account for the appearance of the large number of new particles that have been discovered within the last 40 years.
Although the electron is one of the fundamental particles in nature, we now know that in much the same way that protons and neutrons make up atomic nuclei, these particles themselves are thought to consist of quarks. To give you an idea of the scale of quarks and to illustrate where they fit into the atomic world, a picture showing an atom, nucleus, proton and quark is given below:
In all there are 6 kinds of quark, these are: up, Down, Top, Bottom, Charm and Strange. When physicists talk about quarks they usually put them into three pairs: Up/Down, Charm/Strange, and Top/Bottom. For each of these quarks there is a corresponding antimatter quark (anti-quark). An anti-quark is made of anti-matter. When matter and anti-matter meet, they annihilate each other and their masses are converted into energy.
Quarks always occur in groups of 2 or 3 and are never found on their own. A group of 3 quarks together are called a baryon. Protons and neutrons are both baryons. Protons are made up of two up quarks and a down quark, whereas neutrons are made up of two down quarks and an up quark.
Two quarks together are known as a meson, mesons are made up of a quark and an anti-quark, thus making them extremely unstable. As a group mesons and baryons are collectively known as hadrons. In addition to quarks and electrons there is another fundamental particle known as the gluon. Put simply gluons are the particles that 'carry' the force that holds groups of quarks together. Both quarks and gluons are only found inside hadrons, so we say that they are confined. The quarks inside a hadron are bathed in a sea of gluons (and additional quark-antiquark pairs) that are responsible for the binding forces in the hadron. Quarks continually emit and absorb gluons and the force that the gluon 'carry' is known as the strong interaction. More about the strong interaction and about the other fundamental particles is given in the section on "Quantum Chromo-Dynamics and the Strong interaction."