In this thesis, we study quandles, algebraic structures within knot theory. Following an overview of knots and links, we study knot invariants by focusing on n-coloring of knots and the knot group. Then, we examine the fundamental quandle of a knot, known also as the knot quandle. The knot quandle is stronger and almost complete invariant compared to the knot group. The fundamental quandle of a link is infinite except for the unlink and the Hopf link. However, the n-quandle quotient of the knot quandle is finite for some positive integers n. While studying quotients of the knot quandle, we expound the method of constructing the n-quandle quotient of the fundamental quandle of a knot, including computations of n-quandle quotients of the knot quandle of the trefoil knot for n= 2,3,4,5.