It's 90 KN for entry ticket/adult to National park and you can enter as many times as you wish once you bought it. You can purchase it from a few different locations (Polace, Pomena, and by parking in Pristaniste) and keep it with you for your entire stay.
Price (also) includes boat ride to Sv. Marija island on big lake and 2 tickets for mini bus - we only used the boat ride ticket because you won't really need a van to get around, only if walking makes you tired. But we know that walking has therapeutical properties, but do as you feel.
After some time the monk noticed that water level gets sometimes higer due to a higher tide and that it could flood the monastery. So a smart guy among the monks calculated that if they dig another channel on the other side of the lake the water will flow into another lake. So they did and succesfully solved this tide problem. So, now by the high tide water flows from the sea into Great lake and from here into Small lake and by low tide it turns around.
Fondest memory: Small lake is some 1/4 sq km larg with a maximum depth of 29m.
Big lake is an artificially created lake. In the past the monks from the monastery ruled the island and people had to pay big taxes. People revolted and to protect themselves, monks digged a channel on the eastern part of the valley and let the sea water flood the area. So, the water in the lake is actally salty. As the monastery was built on a hill in the middle of the valley, monastery remaind above water level and the monks eliminated the revolt threat as in those times very few people had boats or could swim.
Fondest memory: The lake is now 1,5 sqkm larg an with a maximum depth of 46m.
Favorite thing: If you want to visit Mljet National Park you'll have to pay admission. It's 90 kunas per person (children below 6 years free). This admission includes the boat trip to St. Mary island and the monestary. The rest is for the maintenance of the park.