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Despite there being many particles made of quarks, there are others which are not. Such particles do not carry strong charge and so do not obey the strong force, and they are referred to as "leptons". Both the electron and positron are leptons, for example, yet there are others which don't even carry electric charge called "neutrinos". As far as we can presently tell, all leptons are truly fundamental, so have no internal constituents whatsoever, simply being points in space with no spatial extent but which carry certain properties that make them more than nothing at all.
Quarks and leptons together explain the entire zoo of material particles, and are together referred to as the "fundamental fermions". There are three so-called "generations" of fundamental fermion, each having two quarks and two leptons, and each being the same as the next generation except for a difference in mass. There is no current evidence for a fourth generation, but the reason why nature is capped at three is currently unknown.
Each fundamental fermion has an antiparticle with opposite properties. The positron has already been introduced as the antiparticle form of the electron, carrying positive electric charge rather than negative electric charge, and the same goes for the antiparticle forms of the other charged leptons. Despite neutrinos being electrically neutral, they too still have anti-partners that are distinguished in other ways. As mentioned in the previous section, an anti-quark carries not only the opposite electric charge to its regular counterpart, but also the opposite strong charge. A quark with positive electric charge and green strong charge therefore has an anti-partner with negative electric charge and anti-green strong charge.
There is nothing particularly unusual about antiparticles, and the lightest generation of antiparticles seem to be just as stable as the lightest generation of regular particles. We can therefore envision making an anti-universe entirely out of the stable antiparticles, with anti-nuclei formed of anti-quarks, and anti-electrons (i.e. positrons) in orbit about these anti-nuclei to form anti-atoms, and these anti-atoms making up anti-stars and anti-planets and anti-everything-else. Physically there is nothing wrong with that at all.
The interesting thing with antiparticles is not that they can exist, but rather what this tells us about the existence of regular particles. When a regular particle meets its antiparticle, their opposite properties cancel each other out and they completely annihilate, with their mass energy converting to light energy and radiating away. In short, particles and antiparticles cannot coexist. However, if particles and antiparticles are true opposites, there should have been no preference for the creation of either class at the time the universe came into being. In that case, as soon as the universe was created, it would have completely destroyed itself in the ensuing annihilation of equal amounts of opposite particle pairs. As we have a universe to talk about at all, that clearly did not happen. This means that there is some kind of preference for the creation of regular particles rather than antiparticles. There is some idea of why this might be, but it remains a big open question.