When I finish fermentation I am left with a large amount of extra yeast in the bottom of the carboy.
Can I reuse this yeast in any way?
Hopefully to avoid buying yeast again every single batch?
You can reuse it, yes. As PMV said, it's usually ideal for a larger batch.
The downside of this is that often this yeast cake will have lots of hops and other trub intermixed within, which can be very bitter, affecting the flavor of the next batch. Generally it's OK to do this if the bitterness levels and yeast profile characteristics are similar. For example, make a hefeweizen on the first batch, then pitch a wort for a weizenbock on the yeast cake.
A better practice to get into is to make starters. Make a starter at least a day before your brew day, with say 75% of the yeast from your store-bought package. Use the other 25% to make up a second, smaller starter that you can then store for future use. This way you're assured of having a clean strain without any possible infections or other weirdness from your yeast cake.
Search for "washing yeast" and you'll find lots of articles and videos showing how to harvest the yeast from a batch and reuse it for a new batch. Every time you do it, you're also carrying over any mutations or changes that colony of yeast has, meaning you can't go too many generations out before the flavors will start to change.
Generally reuse it on a bigger recipe unless you're washing the yeast too. If you already have wort made, just put it right on top of the yeast cake. If not, empty off most of the beer, and dump the yeast into sanitized plastic bottles (glass can break if capped), then put them in the fridge. If you don't have plastic bottles, use glass, but cover them with foil rather than an air tight cap.
I have been kinda laid back in my re-use of yeast cakes on the bottom of the fermenter.
My technique isn't the "Best Practice", but it works and is really easy.
I'll often buy a couple of the same extract kits and do them back to back, when one is done primary fermentation and I've siphoned it into the secondary, then I'll just start the next batch directly on the yeast cake that's sitting at the bottom of the primary.