Particle Physics: the context on the successful yet incomplete theory from start to finish

In the late 1800s chemists were building the periodic table after realizing all these different gases they were studying had a real nice pattern to them. They were organizing them by by weight and valence charge which they realized were a result of these different gases being made up of different numbers of smaller pieces: protons and electrons (and neutrons too). All of the different elements they were discovering were really just combinations of smaller particles. So in the 1900s when physicists were discovering new small particles and organizing them they took inspiration from the chemists a century earlier and realized all of these different particles they were discovering were really just combinations of smaller particles: quarks. They then organized these new smaller particles into our own table: the Standard Model.

Here you should note our friend the electron, a fundamental particle (not made up of other particles) as far as we can tell. You should also note the lack of the proton. The same way you don't see water (H20) on the periodic table, the proton won't appear on the Standard Model. A proton is made of two up quarks and one down quark (uud), similar to how Hydrogen is one proton and one electron. The proton is a composite particle (made of multiple fundamental particles). You can also build the dozens of other composite particles we know of using these quarks in either groups of two like the pion (ud) or three like the proton (uud).

Also note how we've only talked about the first column. For example it's not common to hear about the muon. There's a good reason for this. The muon has a lifetime on the order of a millionth of a second. This means if there's a muon hanging out in the universe if you check on it a few millionths of a second later you won't have a muon anymore, you'll have an electron. Crazy right! The universe can just decide to change that muon into an electron. It doesn't break any rules. The universe wants to because the muon is 200x heavier than the electron and the universe likes to relax down to the lowest energy state. Think of how much harder it is to hold a bowling ball at arms length as compared to a penny. The universe is lazy, so if it is allowed to make its life easier it will. So a muon will decay down into an electron pretty quickly. Even better if you have a tau, the electron's cousin that is 2000x heavier than it, who will live less than a trillinth of a second. The universe doesn't like holding a teenager at arms length. This rule goes for all the particles in the Standard Model. That's why you've heard of a proton but you probably haven't heard much about the sigma particle (uus), the protons heavier and therefore shortly lived cousin. Or why I'll talk about the pion (ud) and not the kaon (us). 

Particle physicists like speaking in terms of a special kind of diagram called Feynman Diagrams. Below is the Feynman Diagram of the muon decaying to an electron (and releasing some neutrinos in the process)

We read these diagrams from left to right, where the initial particle (the muon) is on the left, and the final state particles (the electron and neutrinos) are on the right.

Let's keep the going with the parallels to chemistry. In chemistry you'll often see something like this:

where you don't change the number of H's nor the number of O's. You started with 2*2 = 4 H's and 1*2 = 2 O's and you ended with the same 2*2 = 4 H's and 2*1 = 2 O's. Effectively you're just moving the protons and electrons from place to the other, conserving things like mass.

In particle physics we have different rules. Most notably, we don't need to conserve mass.

Einstein told us this is in probably the most famous equation ever. But what does it mean?

Let's day I have a ball of stuff that has a mass of 10. I could do some stuff to make two things of mass 5, no worries. More excitingly, if I can find a way to completely annihilate that ball of stuff I can get an energy of 10 from it leaving no mass behind (no mass can be weird to think of, so try and think of light which carries energy but has no mass). 
We can go vise versa too! If I have an energy of 10 from that I can make a ball of mass of 10. OR. I can make 2 balls of 5. Or 10 balls of 1. Mass is not something that needs to be conserved in particle physics, just energy. Mass is just a way to store energy, the same way that raising the bowling ball off the ground gives it energy and when you release it that energy can be converted into kinetic energy (energy of motion).

This is very powerful. If I have a ball of mass of 10 that is stationary I can only make stuff that is 10 or less. BUT. If I get that ball of mass 10 moving at an energy of 5 I can then make something of mass 15! Remember, mass is just stored energy the same way that movement is stored energy. If I get that same ball of mass moving at an energy of 90 I can make something 10x heavier than the thing I am using to make it!

This is the idea behind particle accelerators like the LHC!