A survey on positive mass theorem? Could you suggest a good survey paper on positive mass theorem?
 A: Maybe Markus Khuri's RTG notes would help? 
There's also a set of lecture notes by Rick Schoen for his 2009 course in Stanford on General Relativity, which has a nice discussion of the fundamental ideas involved in the proof of the PMT. I don't know if it is publich available on the internet though...
A: H. Bray's articles "Black Holes, Geometric Flows, and the Penrose Inequality in General Relativity" (Notices AMS, 2002) contains a very short, but elegant, survey of the positive mass theorem. He also has a longer survey that goes into several simpler cases.
A: Lecture notes (2009) by Rick Schoen on Relativity :
http://math.stanford.edu/~schoen/trieste2012/ 
A: Dan Lee's book Geometric Relativity available here: https://bookstore.ams.org/gsm-201/
A: Not a survey per se, but a good article on the theorem is the one below which gives a quick, clear sketch of the second part of Schoen and Yau's proof of the positive mass theorem.
It might be helpful to read this before reading the second part of the proof in order to not get lost in the details, especially if one does not have a background in PDE analysis.

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*Schoen R and Yau S-T 1979 Positivity of the Total Mass of a General Space-Time.  Physical Review Letters 43, 20

