  We present new quasars discovered in the vicinity of the Andromeda and
Triangulum galaxies with the LAMOST during the 2010 and 2011 observational
seasons. Quasar candidates are selected based on the available SDSS, KPNO 4 m
telescope, XSTPS optical, and WISE near infrared photometric data. We present
509 new quasars discovered in a stripe of ~135 sq. deg from M31 to M33 along
the Giant Stellar Stream in the 2011 pilot survey datasets, and also 17 new
quasars discovered in an area of ~100 sq. deg that covers the central region
and the southeastern halo of M31 in the 2010 commissioning datasets. These 526
new quasars have i magnitudes ranging from 15.5 to 20.0, redshifts from 0.1 to
3.2. They represent a significant increase of the number of identified quasars
in the vicinity of M31 and M33. There are now 26, 62 and 139 known quasars in
this region of the sky with i magnitudes brighter than 17.0, 17.5 and 18.0
respectively, of which 5, 20 and 75 are newly-discovered. These bright quasars
provide an invaluable collection with which to probe the kinematics and
chemistry of the ISM/IGM in the Local Group of galaxies. A total of 93 quasars
are now known with locations within 2.5 deg of M31, of which 73 are newly
discovered. Tens of quasars are now known to be located behind the Giant
Stellar Stream, and hundreds behind the extended halo and its associated
substructures of M31. The much enlarged sample of known quasars in the vicinity
of M31 and M33 can potentially be utilized to construct a perfect astrometric
reference frame to measure the minute PMs of M31 and M33, along with the PMs of
substructures associated with the Local Group of galaxies. Those PMs are some
of the most fundamental properties of the Local Group.
