  This dissertation consists of three parts. The first part of the thesis is
devoted to the study of gravity and higher spin gauge theories in 2+1
dimensions. The first part deals with cosmological solutions of spin-3 gravity
and their thermodynamics, flat space limit of AdS$_3$ gravity and higher spins
using Grassmann approach and chiral higher spin solutions with the most general
AdS$_3$ boundary condition. The second part is devoted to the problem of
Neumann boundary condition in Einstein's gravity. We present an explicit
boundary term that makes the Neumann variational problem well posed and explore
its consequences for holography in various dimensions. In the third part of the
dissertation, we use the CFT techniques of Rychkov and Tan to compute anomalous
dimensions in the O(N) Gross-Neveu model in $d=2+\epsilon$ dimensions. To do
this, we extend the "cow-pie contraction" algorithm of Basu and Krishnan to
theories with fermions.
