To overlook is to unintentionally ignore someone or something. 

I took presents for the children of Jeff, Michael, and John, but I completely overlooked the children of Frank.  What was I thinking of?  I certainly did not mean to ignore them.  I was busy and somehow I forget all about them.

While making plans for my vacation, I overlooked the fact that the rainy season was approaching and that outdoor activities would be difficult.  How could I forget something that important?

To take for granted is to assume something.

My grandparents, parents, and all my siblings played the piano.  It was taken for granted that I would play it to, but I was never interested in music.  The assumption was wrong.

Since you and Zeca are sweethearts, I take for granted that you are going together to the party on Saturday.  Am I correct in assuming that?

With all this rain, may I take for granted that you will be taking an umbrella?