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Is there a user friendly exposition of the notion of boundary of an Alexandrov space with curvature bounded from below and of the Doubling theorem?

The only reference I am aware of is the original preprint by Perelman which is not very user friendly to my taste (though I am not an expert in the area).

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    $\begingroup$ Perelman's doubling theorem is generalized in [S.Alexander and R.Bishop "Curvature bounds for warped products of metric spaces, (GAFA) 14 (2004) 1143-1181.] See math.uiuc.edu/~sba/wp.pdf. $\endgroup$
    – Igor Belegradek
    Commented Aug 29, 2015 at 21:45
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    $\begingroup$ @IgorBelegradek it uses the doubling theorem. $\endgroup$
    – Anton Petrunin
    Commented Jun 29 at 23:22

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You may check our draft: "A journey into Alexandrov geometry: curvature bounded below" by Vitali Kapovitch and me. It is based on a graduate course. We do not pove Perelman’s theorem about conic neighborhood; the rest is nearly rigorous

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