In this thesis, we review some basic properties of the Einstein-aether gravity. We derive the field equations from an action and study a subclass of this theory corresponding to the Einstein-Maxwell like theory. We also show that the G&ouml / del type metrics are also exact solutions of this theory. Furthermore, we determine the observational constraints on the dimensionless preferred parameters of this theory using the parametrized post- Newtonian formalism. We stress that none of calculations and discussions are original in this thesis.