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ABSTRACT: Let $C$ be an integral projective curve of arithmetic genus $g \geqslant 2$ over the field of complex numbers and let $E$ be a vector bundle on $C$. The Quot scheme $\text{Quot}_{C}(E,k,d)$ parametrizes quotients of $E$ of rank $k$ and degree $d$. Quot schemes play a central role in understanding the geometry of moduli spaces of sheaves and have important applications in enumerative geometry. In this talk, we will discuss geometric properties of the Quot scheme $\text{Quot}_{C}(E,k,d)$, focusing on irreducibility and singularities. We will also see results on Nested Quot schemes which parametrize chains of successive quotients.