@mastersthesis {2007, title = {Noncommutative geometry and quantum group symmetries}, year = {2007}, school = {SISSA}, abstract = {It is a widespread belief that mathematics originates from the desire to understand (and eventually to formalize) some aspects of the real world. Quoting [Man07], {\guillemotleft}we are doing mathematics in order to understand, create, and handle things, and perhaps this understanding is mathematics{\guillemotright} . Let me thus begin with a brief discussion of the physical ideas that motivated the development of Noncommutative Geometry and Quantum Group Theory - the areas of mathematics to which this dissertation belongs. Some physicists believe, and Einstein himself expressed this view in [Ein98a], that physics progresses in stages: there is no {\textquoteleft}final\\\' theory of Nature, but simply a sequence of theories which provide more and more accurate descriptions of the real world...}, keywords = {Noncommutative geometry}, url = {http://hdl.handle.net/1963/5269}, author = {Francesco D{\textquoteright}Andrea} }