After a bit of research I discovered that it was the famous, Roman Snail, or as the French refer to it as Escargot. This is the common edible snail native to limestone areas of central and south-eastern Europe. The parks and yards of Belgrade are full of them. This morning on my run with Ocean (a later post), I saw two old men collecting them in the park. This afternoon I saw a woman also collecting them down the block.
They are called the Roman Snail because the Romans used to eat them too. The scientific names is Helix pomatia and it is also known as the Burgundy Snail, from the Burgundy region of France. They can do damage to trees and garden plants.
I have to try these, perhaps if the wet weather persists, we’ll collect a bunch. From ehow.com website I copied the recipe on how to prepare them:
Preparing Live Snails
Step1
Put the snails in a container without any food for 2 days. Wash them frequently to rid the snails of any toxins and empty their intestines.
Step 2
Remove the snails from the container and again wash them thoroughly. Either boil them for a short period of time or put them in the freezer to kill them.
Step3
Remove the snails from their shells using tweezers or a hook.
Step4
Remove the intestines and the body of the snail. You only want to eat the foot. The internal organs are not tasty.
Step5
Take off the shell door (the operculum) of each snail. If you want to reuse the snail shell to prepare an appetizer, sterilize them by washing them thoroughly with baking soda, rinsing them repeatedly and boiling them.
I wonder what the Serbs call them? Any Serb readers know?
Bill's Blog 
We call them puzevi.
Snail – puz
Snails – puzevi