We once thought that atoms were the basic building blocks of the universe. Then, we discovered that atoms are composed of protons, neutrons, and electrons. For several decades we thought that these were the basic building blocks, but starting in the 1960's we discovered that protons and neutrons are composed of even smaller particles called "quarks".
The field of physics dedicated to understanding the fundamental constituents of the universe is called "elementary particle" physics. This field emerged from nuclear physics, and nowadays shares common interests with nuclear physics, astrophysics, and even atomic physics.
All known particles fall into three categories: quarks, leptons, and gauge bosons. The quarks and leptons are of a class called fermions, and are the basic constituents of all matter. The gauge bosons are the carriers of force.
The proton and neutron are composed of quarks, specifically, "up" and "down" quarks. The distinguishing feature of quarks is that they "feel" the strong force, the force which binds the up and down quarks into protons and neutrons, and is discussed later. In addition to up and down quarks, we have discovered four other quarks, known as "strange", "charm", "beauty" or "bottom", and "top". We normally indicate the quarks with the lower case letter at the start of the name, so we have d, u, s, c, b, t. (The b quark is often called bottom, because it is naturally paired with the top quark. However, people studying processes involving the b quark prefer to refer to it as "beauty physics"; the term "bottom physics" too closely resembles the deragatory term "bottom feeders".)
The six quarks separate into two groups with different electric charge: u, c, and t have charge +(2/3)e, and d, s, and b have charge -(1/3)e. There is also a natural progression in mass. The u and d quark are relatively light, the c and s quarks are intermediate in mass, and the b and t quarks are heavy. The t quark is the heaviest of all. The mass of a single t quark is roughly equivalent to the mass of an atom of gold, 175GeV. Due to its large mass, the t quark was the last to be discovered. It was first observed in 1995 at Fermilab, a major national research laboratory about 40 miles from Chicago.
Electrons fall into the lepton category. Leptons are fermions that don't feel the strong force. The other leptons are the muon, the tau, and three "neutrinos", the electron neutrino mentioned in beta decay, the muon neutrino, and the tau neutrino.
The neutrinos have zero charge, and zero or extremely small mass. This combination makes them very hard to detect, they don't interact electrically, and their weak interactions are, well, weak. Yet they are so abundant, that if they have even the miniscule mass of a fraction of an eV (about one-millionth the mass of an electron), their mass would roughly equal the mass of all the atoms in the universe! If we want to understand the universe, then we must understand neutrinos.
The electron, muon, and tau are charged leptons with charge -1e. These particles are basically identical except for their masses. The muon and tau are sometimes referred to as heavy copies of the electron. Why nature has two additional copies of the electron is still a mystery.
In our present view of the world, force is due to the exchange of a particle from the category of "gauge bosons". To every force there corresponds a gauge boson, and to every gauge boson a force. The idea is something like two ice skaters tossing a mass between themselves. When skater 1 throws the mass, she is pushed in the opposite direction so that momentum is conserved (momentum of skater 1 = -momentum of mass). When skater 2 catches the mass, he is also pushed, this time in the direction of the moving mass. In the case of the exchange of gauge bosons, the idea is similar except that, through the magic of Heisenberg's uncertainty principle, the force can be attractive or repulsive!
We have already encountered one of the gauge bosons, the photon. The photon is the "carrier" of the electromagnetic force -- both the electric and magnetic force. The photon is massless, and susceptible only to gravity.
Having mentioned gravity, it's gauge boson is called the graviton. The graviton is extremely interesting, but it's most important role is in astrophysics, and string theory. I won't discuss it further.
The next gauge boson goes by the name "gluon". The gluon is the carrier of the strong force which binds the quarks into protons, neutrons, and similar particles. The name comes from the picture of binding the quarks with "glue", making it basically impossible to have a single free quark. While there is basically one photon and one graviton, there are 8 different gluons.
The final gauge bosons are a triplet known as the weak bosons because they carry the "weak" force responsible for beta decay. These bosons are known as W+, W-, and Z0. Many of the modern advances in particle physics are due to studying these 3 bosons.
The modern picture of forces is of an exchange of a force carrying particle between two other particles. We recognize 4 fundamental forces in the universe.