Creating a Partial Vacuum with Water and Air

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when we fill a container with water so as to leave some space above the surface of water. And we close the container. When we turn the tube upside down. The air which which was above the surface of water transfers to the other side. How does this happen. Does air penetrate water?
And suppose we fill a container with water. And pump air into it, how is a partial vacuum created in it?
 
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Do it slowly and you'll see the air either going up slowly as a bubble or going along the side.