How to check laptop-battery compatibility ?

I want a better battery for my Acer Aspire 5532. Current one is AS09A61. So how do I know which battery will work on this laptop ?

This is a 6 cell/4400mAh battery. Check the Acer site to see if they offered optional 9 cell / 12 cell batteries for the 5532 (doesn’t look like it), or look for third party batteries.

No, no batteries for 5532
And any tip to where to look for third party batteries ?

Amazon/Ebay. You need to check feedback since they will largely be from China, so quality can vary.