Can I Crack My WPA Without Aircrack-ng?

Is it possible to crack my WPA without the use of a cracking program like aircrack-ng? Couldn’t I capture packets, identify the IV packets and attempt to crack the hash myself? Is this too ambitious? I’d like to know how to do it this way, because although tools like Aircrack-ng can be helpful, whats the point if you don’t know the theory behind it?

Is this possible?