Here's the basics of what you need to know...
To put everything into perspective, keep in mind that when it comes to all grain brewing water is important in order to mash at the right pH levels (between 5.1 and 5.4 measured at mash temperature, slightly higher if measured at room temperature)
Ok.. so hardness is important to have for mashing and fermentation... hardness is determined by minerals like Calcium, Magnesium, etc.
You want to be in the 50 - 150 ppm for Calcium and 10-30 for magnesium... but not necessarily...
These minerals bring the pH of your mash down, and that's good when you are brewing light beers...
When you are brewing dark beers, the acidity of the dark toasted malts bring the pH down as well, and if you couple that with the minerals that cause hardness, then your pH may be too low (below 5.1) during the mash and your starch to sugar conversion may not be as efficient...
So that's one aspect...
You then have to take into account the alkalinity of the water... Alkalinity comes from your carbonates (i.e. bicarbonate)... these ions raise the pH of the mash...
Alkalinity in this case is bad for your light beers, but good for dark beers because it balances the acidity of dark malts, you follow?
So, what you need to do is... Since your water report doesn't list Alkalinity as CaCO3, you're going to have to call the city's water department and ask to speak with one of the engineers and get that number...
Since you don't have it, I'll use the example above... they have listed:
Total Hardness, CaCO3 124
Total Alkalinity, CaCO3 79
Here's what these two numbers together mean... this water is probably good for your mid-range beers and some darker ones... neutral pH of water is 7... according to the guy above the pH of his water is 7.8... (pH of the water itself doesn't matter as much as the pH of the mash when the grains have been soaking in water for at least 15 minutes)
If you were to try to brew a light beer with this water, the alkalinity will probably make the pH of your mash be too high... you could try simply adding Calcium Sulfate or Calcium chloride to make the calcium bring the pH down... 1 to 1.5 tsp is way more than enough, prob .5 tsp is all you need... however, if that doesn't bring the pH down to where you need it, then you'll have to get rid of the alkalinity somehow...
One way to get rid of alkalinity is to boil, and the way alkalinity is removed when boiling is by combining with minerals like calcium to form calcium carbonate (a.k.a. Chalk)...
... and that's what I meant by comparing hardness as CaCO3 and alkalinity as CaCO3... if your hardness as CaCO3 (meaning calcium, magnesium, etc.) is higher than your Alkalinity as CaCO3 (meaning your carbonates), then you can pretty much get rid of all your carbonates since there is enough minerals to form chalk and still have some leftover for your brew (cause remember you need at least 50 ppm of calcium)... that's good if you want to brew light beers...
If on the other hand your Alkalinity as CaCO3 were to be higher than your Hardness as CaCO3, then you will have 'residual alkalinity' because there is not enough minerals like calcium to form chalk...
that's one issue... the second issue is that you will use up most of your calcium trying to get rid of alkalinity and you need at least 50 ppm of calcium to have a healthy mash and fermentation... that's not good for light beers...
In this case, to reduce all the alkalinity you may need to add more calcium to the water, treat it with slaked lime or lactic acid, dilute it with distilled water or just stick to brewing darker beers...
So that why you really need to get Alkalinity as CaCO3 from your city's water department... so you know if you can get rid of alkalinity by boiling your water...
Whether you want to get rid of alkalinity or not depends on the beer you are brewing... for light colored beers, absolutely... for dark colored beers you probably don't want to get rid of it unless you have too much... and if you don't have enough, you may even need to add a little bit of alkalinity...
I hope that makes more sense...
PS... Alkalinity is sometimes give in the form of HCO3 (a.k.a. bicarbonates)... if that's the case then Divide HCO3 by 61 ad multiply by 50 to get Alkalinity as CaCO3
Cheers!