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Integrating general relativity within a quantum framework could offer promising explanations for the birth of our universe and address various observational phenomena. In this seminar, I will explore two primary approaches to quantum cosmology: the Wheeler-DeWitt equation method and the path integral formulation. Our study focuses on the Bianchi type I anisotropic model, incorporating a scalar field minimally coupled to Einstein-Hilbert gravity, along with a perfect fluid matter sector that introduces a dynamic aspect of time. We begin by quantizing the theory using the Wheeler-DeWitt method, resolving the issue of non-unitarity to construct a well-behaved wavefunction for the universe, potentially eliminating the Big Bang singularity. Additionally, we investigate the Kantowski-Sachs anisotropic cosmological model using the Lorentzian path integral method. In this context, we examine the Hawking-Hartle no-boundary proposal. Our analysis of massless scalar perturbations reveals that large fluctuations are favored, suggesting that any initial perturbations at the beginning of time would flare up at the final boundary. |