The world, then, consists (at least at low energies) of up and down quarks, electrons and (electron) neutrinos.
These particles interact with one another via a variety of interactions or `forces'. Charged particles (and those with magnetic moments) can of course interact via the familiar electric and magnetic forces. In large enough clumps of matter, the gravitational force will make itself felt. Additional forces are encountered at the submicroscopic level.
From the point of view of quantum field theory, an interaction between two particles can be viewed as the exchange of some intermediary particle which mediates the force. The exchange of a massless particle results in a long-range force. Exchange of a massive particle results in a short-range force, with the range of the force depending on the mass of the exchanged particle.
Quarks, as mentioned, interact via the colour force. In addition, there is a weak interaction which is related at a deeper level to the electromagnetic force (the `electro-weak interaction'). This also can be viewed as the interchange of bosons, specifically the massive Z and W bosons. The most striking manifestation of this force in nuclear physics is a transition between up and down quarks which results in a transition between neutrons and protons known as beta decay.
The forces which hold the quarks together in the nucleons are understood (to some extent). The exact nature of the nucleon-nucleon interaction is unknown (i.e. it cannot yet be derived from the underlying QCD), and we rely on complicated parameterised models.
There are a variety of particles that are made of quarks, besides the nucleons. These fall into two categories, the baryons which are fermions and the mesons which are bosons. The residual of the colour force that these particle feel is known as the strong (nuclear) force. These two categories of strongly interacting particles form the hadrons. The light fermions, which do not feel the strong interaction, are known as leptons (the electrons, neutrinos, etc).
The current view of physics, then, is based on this standard model which sees the world as essentially made up of four types of particles:
Each particle has an associated antiparticle. In addition, this pattern is triplicated: there are three families of particles with similar properties but increasing masses.
These additional families play no rôle in nuclear physics (except perhaps at very high energies). In fact, there is no evidence in traditional nuclear physics to support the quark substructure of nucleons. We can understand the properties of nuclei entirely in terms of nucleons and the forces between them. The nuclear forces can be viewed as the exchange between nucleons of various types of mesons (strongly interacting bosons consisting of quark-antiquark pairs).