I worked on linear and weakly non-linear theories on magneto convection in a rotating fluid with isotropic/anisotropic diffusivities using analytical methods. In linear stability analysis, we have determined the marginal stability curves at the onset of stationary and oscillatory convection using one-term Galerkin method. In weakly nonlinear analysis, a two dimensional non-linear amplitude equation near the onset of stationary and oscillatory convection has been derived. Conditions for the occurrence of secondary instabilities such as Eckhaus and Zigzag instabilities are studied. Also,...