Wang, Victor Zhenyi2019-10-102019-10-10http://hdl.handle.net/1885/173669In 2000, Fomin and Zelevinsky introduced a new language called cluster algebras for describing rings with certain combinatorial structures. Cluster algebras enjoy a variety of nice properties such as well-established collection of classification results and interesting geometric properties with the upper cluster algebra. We approach cluster algebras rst from the perspective of operations on quivers, then reacquaint ourselves with a more general definition. We then present the classification of cluster algebras of nite type and explore cluster algebra structures on the ring of regular functions of double Bruhat cells.application/pdf201610.25911/5d9efbd8776462019-10-10