Quadratic curvature gravity theories in various dimensions with and without torsion

In this thesis work, generalized gravity models are examined in n-dimensional spacetimes. Generalized gravity theories are described by a Lagrangian that involves a gravitational function expressed in terms of the scalar curvature, Ricci-squared and Riemann-squared terms in general. The models are investigated for two seperate cases, in which the connection of the spacetime is torsion-free and the connection of the spacetime involves spacetime torsion. By using exterior algebra formalism, the field equations of the theory are obtained by making independent variations of the gravitational action with respect to metric co-frame and connection fields. 3-dimensional gravity models such as Topologically Massive Gravity, New Massive Gravity, Minimal Massive Gravity and Generalized Massive Gravity are examined within the same framework. For certain generalized gravity models, some new exact solutions are achieved. Among them are the constant curvature solutions of quadratic curvature gravity model in a spacetime involving torsion. In addition, Lifshitz-type and Bianchi-type static and stationary solutions and Schrödinger-type solutions of R2-corrected gravity model are presented. Also, pp-wave solutions of Minimal Massive 3D Gravity theory are examined for both vacuum case and for the gravity model that is minimally coupled to Maxwell-Chern-Simons electromagnetic theory.