Recently I've been learning about RFID tags and readers. I bought the MFRC522 reader and some tags. I know there are a couple of libraries out there, but I decided to implement my own. Also, I think the existing libraries are too coupled messing around the reader API with the tag API.
This is the library I created: GitHub - dalmirdasilva/ArduinoRadioFrequencyIdentification: Arduino Radio-frequency identification
There are a bunch of examples too. The MFRC522 reader and the Classic Mifare tag are fully implemented.
Feel free to improve it or just use it!
Hope it helps someone.