Well done, Dave!

Two important additions:

1) Chlorine's MOST important target, even more so than algae, is fecal matter--poop. It neutralizes and renders safe the contaminants in fecal matter, the most dangerous pollutant in your pool water. Chlorine is the only sanitizer we can be sure of to neutralize these dangerous contaminants.

When contaminated drinking water is responsible for outbreaks of people getting typhoid, typhus, cholera, etc., the contaminant spreading it is INEVITABLY fecal matter.

2) Stabilizer or CYA, while absolutely necessary, is a two-edged sword. As Dave points out, you must have it to prevent rapid breakdown of chlorine, but too much can prevent chlorine from doing its job. It's very important to use the "Best Guess Table" to determine how much chlorine you need for a given level of stabilizer.

(as an aside, do NOT use stabilizer with indoor pools. Check with PoolDoc on indoor pool management rules)