  In this report I will give a summary of some of the main topics covered in
Session A3, mathematical studies of the field equations, at GRG18, Sydney.
Unfortunately, due to length constraints, some of the topics covered at the
session will be very briefly mentioned or left out altogether. The summary is
mainly based on extended abstracts submitted by the speakers and some of those
who presented posters at the session. I would like to thank all participants
for their contributions and help with this summary.
