The cost of a student monthly ticket (tram&bus) is 53 PLN (13 EUR).
The Krakowska Karta Miejska (KKM) is a card for city transportation which you can buy in any MPK outlet (for example at Podwale Street 3/5) and extend its validity in any ticket machine.
The best option is to purchase a semester ticket which costs 220 PLN (52 EUR).
The transportation card can be registered digitally on the student ID card.
Navigation in mobile app
Jak dojadę is a popular Polish website and mobile app that finds the quickest and most convenient public transport connections. The website is also available in English.
You may use either the website or download application from app shop.