Quark-Gluon Plasma and Relativistic Heavy-Ion Collisions --An Overview and Recent Advances

In the first part of the talk, I will present an overview of the field of quark-gluon plasma and ultra-relativistic heavy-ion collisions. I will describe the most important observables and their status in the current experiments at the Large Hadron Collider, CERN. I will highlight the important role the relativistic dissipative fluid dynamics is playing in describing the flow of the matter formed in these collisions. In the second part of the talk, I will describe a new method which allows extraction of event-to-event flow fluctuations directly from experimental data. It is based on the Principal Component Analysis (PCA) technique applied to the two-particle correlation matrix. PCA has revealed subleading modes in multiplicity, elliptic flow, and triangular flow fluctuations for the first time.