  The aim of this proceeding is to give a basic introduction to Deformation
Quantization (DQ) to physicists. We compare DQ to canonical quantization and
path integral methods. It is described how certain issues such as the roles of
associativity, covariance, dynamics, and operator orderings are understood in
the context of DQ. Convergence issues in DQ are mentioned. Additionally, we
formulate the Klein-Gordon (KG) equation in DQ. Original results are discussed
which include the exact construction of the Fedosov star-product on the dS and
AdS space-times. Also, the KG equation is written down for these space-times.
This is a proceedings to the Second International Conference on Quantum
Theories and Renormalization Group in Gravity and Cosmology.
