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Hi I want to study harmonic measure for planar domain and its extension to higher dimension,could you tell me some books/papers on this topic starting from elementary?

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    Your original title for this question was just "reference request". I changed it to something more specific. It should be possible to see from the title what the question is about, so that people can look at the questions they're interested in and/or that they can answer. Concerning the fact that you haven't got any answers to this question, you might consider attributing that at least in part to the fact that you haven't accepted a single one of the answers you were given previously. I see that Qiaochu already made you aware of this in early March.2011-04-13

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A very nice book for a beginner is Potential Theory in the Complex Plane by Ransford. Much more in-depth treatment of the planar harmonic measure is in Harmonic Measure by Garnett and Marshall.

The theory has a different flavor in dimensions $n\ge 3$ where complex analysis does not help and the results are less complete (as far as I remember, the precise range of Hausdorff dimension of harmonic measures remains unknown). I can recommend Potential Theory in Modern Function Theory by Tsuji and Subharmonic functions Volume 1 by Hayman and Kennedy.