The original battery in my MBP had swollen to the point that I couldn't click on the trackpad. Not to mention the capacity was, at best, half of its original capacity.
I then bought an Apple replacement battery from iFixit. In about a year, that one also became swollen like the original one. But, by then, iFixit was no longer selling Apple batteries, so I bought a third party battery.
The repair process itself is trivial. I didn't even need the guide. The third party battery looks fairly like the original one and fits well.
Unfortunately the capacity of the battery is an entirely different matter. I don't think this battery ever had its guaranteed 5510 mAh capacity, and after a few months it's gotten even worse. I can barely get 2-2.5 hours of use out of it, but what's worse is that the battery level suddenly drops from 40-50% to 7% AND the battery recharges extremely slowly.
Are you also content with your early 2011 MacBook Pro that still functions perfectly except its battery? Well, too bad. Your laptop has been obsoleted. Don't expect to get much out of the replacement battery in terms of usage time.
But you may still need this replacement battery because your current one is swollen and doesn't let you click. Or it might be completely dead, in which case your laptop will run at a third of its CPU power. (My thanks to Apple for not providing enough power from the power adapter to run the computer at full speed without a battery.)