Is there oxygen in water?

Absolutely!  Living organisms in lakes, rivers, streams, and oceans require oxygen to survive!  Dissolved oxygen is one of the most important factors in an aquatic environment.  
 

How can oxygen be in the water?

Water, like air, is a mixture of compounds.  Air consists of mostly nitrogen (about 78%) and some oxygen (about 21%).  Water is also a mixture.  While the overwhelming majority of water is composed of water (H₂O) molecules, gases become trapped among these water molecules.  Mammals that live on land have lungs that are adapted to extract oxygen molecules from the air.  Fish and some aquatic insects need a slightly different mechanism for extracting oxygen from the water, and that is why they have gills.  Oxygen is much less abundant in the water.  Air consists of 21% oxygen, but the oxygen content in water is only 0.001%!  Therefore, gills need to be much more efficient than lungs in extracting oxygen. 

Have you ever mixed sugar or salt in a glass of water?  If you have, you know that the sugar or salt will disappear as it dissolves in the water; unless you mix a very large amount of sugar or salt in the water and exceed the ability of the water to dissolve these substances.  In a similar manner, oxygen dissolves in water.  When oxygen molecules are mixed with water molecules, attractive forces suspend the oxygen molecules between water molecules.  The attractive forces keep the oxygen together with the water molecules and prevent its escape from the water.