Capacitor / inductor resonance I understand that a inductor builds up a charge on it, then the current flows to the capacitor, charging it. But then once the capacitor has stopped current flow and the capacitor is about to discharge why does it charge the inductor back up? As the inductor is positioned in the circuit before the capacitor why would the current flow the "wrong way" around the circuit to charge the inductor? Wouldn't it have to go all the way around the circuit first?
Does a capacitor discharge in the opposite direction to charging or something? 
 A: At t=0, $i=0$ and the capacitor is charged with a given energy $$E_{capa}=\frac{1}{2}CV^2$$
where $V$ is the voltage at its terminals. Since the circuit has two elements, the inductor shares this voltage. However, $$V=L\frac{di}{dt}$$
thus the current increases. The capacitor gives its energy to the inductor : $$E_{ind}=\frac{1}{2}LI^2$$
and the voltage decreases until there is no more current variation, i.e. $V=0$. However, $$i=-C\frac{dV}{dt}$$, thus the voltage keep decreasing (negative voltage) until the current is exhausted.
The energy is exchanged between the inductor (magnetic) and the capacitor (electric). It's really like a ball falling along a U shape.
A: 
I understand that a inductor builds up a charge on it,

The energy stored by an inductor is proportional to the square of the current through.  No electric charge builds up on an inductor.

then the current flows to the capacitor, charging it.

For a simple LC circuit, there is just the series current which is through (not to) both the inductor and capacitor.

But then once the capacitor has stopped current flow and the
  capacitor is about to discharge why does it charge the inductor back
  up?

For an inductor, the voltage across is proportional to the rate of change of current through.
The greater the voltage across, the greater the rate of change of current.
Since, in a simple LC circuit, the capacitor and inductor have the same voltage across, as the voltage increases on the capacitor, the current changes at a faster rate.  When the current is zero, the capacitor (and inductor) voltage is maximum which means that the current is changing most rapidly there, i.e., the current goes through zero and changes direction.

As the inductor is positioned in the circuit before the capacitor why
  would the current flow the "wrong way" around the circuit to charge
  the inductor?

There is no wrong way around the circuit.  The direction of current can be clockwise or counter clockwise around the loop.

Wouldn't it have to go all the way around the circuit first?

I have no idea what you're thinking here.  The electric current is throughout the circuit, i.e., the flow of charge is (ideally) the same everywhere along the circuit.  

Does a capacitor discharge in the opposite direction to charging or
  something?

When a capacitor is charging, current enters the more positive terminal (exits the more negative terminal).  When discharging, the current exits the more positive terminal.
