In this thesis, we introduce new theories of bi-gravity. We know that general relativity cannot predict some observations beyond the solar system. So besides some theoretical problems, we need to modify general relativity. One of the theories which tries to solve these problems is massive gravity. However, by giving mass to graviton, the problem of ghost (extra degree of freedom with negative kinetic energy) and non-unitarity arises. The efforts to introduce a consistent theory for massive graviton has a long history. However, it is believed that a fully non-linear consistent theory of massive gravity has been achieved. Moreover, a theory with two metrics known as “bi-gravity” is suggested which seems to be consistent with unitarity and includes interesting cosmological solutions. There are also higher derivative theories which have been introduced in three dimensions as quantum gravity candidates. However, due to logarithmic modes in their spectrum, they fell down to the non unitarity problem. One of these theories is “new massive gravity” (NMG) which has one massive graviton and one massless graviton in its spectrum. This theory cannot pass the unitarity test in the bulk and on the boundary simultaneously. This problem is known as “bulk-boundary” clash. In this thesis, we focus on solving this problem. Using the action of NMG, we construct a new bi-gravity in three dimensions. This is done by promoting the rank two auxiliary field appearing in the expression of NMG’s action into a dynamical field. We show that small fluctuations around the AdS vacuum of the model are non-tachyonic and ghost free within a certain range of the parameters of the model. We study central charges of the dual field theory and observe that in this range they are positive, too. This suggests that the proposed model might be a consistent three dimensional bi-gravity. Another important point is higher derivative gravity theories in higher dimensions. This extension for NMG theory is known as “critical gravity”. However, the similar non-unitarity problem occurs again. In this thesis, we discuss how our model can be extended to higher dimensions in order to solve this problem. These new bi-gravities, at the linear level around the AdS vacuum are free of the Boulware-Deser ghost, kinetic ghost and tachyonic instability within the particular range of parameters. Moreover, we show that the energy and entropy of AdS-Schwarzschild black hole solutions of these new models are positive in the same range of parameters. This may be the sign that these new models are also