P.S. And just to give you a preview of things you'll be learning in the future, I would venture to say that there are maybe 4 really crucial and major functions of the Russian genitive:

(1) possession
(2) absence or non-existence
(3) part of something consumable ("a bit of tea"; "some of the bread")
(4) separation or movement away from

The genitive can cover other concepts, but the above four are probably the most important ones.

And some linguists argue that the real underlying meaning of the Russian genitive is (4) "separation; movement away", and each of the other three are "special cases of separation" -- thus (1) is "an owned object considered separately from its owner"; (2) is "separated from the category of things that exist"; and (3) is "a part separated from the whole."