<p>This study analyzes a Leslie-Gower predator-prey system with diffusion, governed by a ratio-dependent Holling type III functional response under Neumann boundary conditions. By linearizing the system at the positive equilibrium and studying the associated characteristic equation, we establish criteria ensuring local stability and determine parameter conditions that lead to a Hopf bifurcation at the coexistence state. The stability properties of the periodic orbits emerging from the bifurcation are further investigated in the spatially homogeneous case without diffusion. In the spatially extended system, the role of diffusion is examined with particular emphasis on diffusion-induced instabilities. Specifically, the conditions for the emergence of Turing instability and diffusion-driven Hopf bifurcation are derived. Finally numerical simulations are added to verify the theoretical results.</p>