We will give an introduction to shifted symplectic geometry of Pantev, Toen, Vaquie, and Vezzosi (PTVV) as featured in their article http://arxiv.org/abs/1111.3209. As this article is technically challenging, we will focus on examples and try to give the audience a flavor of how one can think about these objects without needing to understand all details of that article. Shifted symplectic geometry is the study of certain generalizations of algebraic varieties called derived stacks which are equipped with an extra structure called an n-shifted symplectic form. Here n can be any integer but a particular example of a 0-shifted symplectic derived stack is simply a smooth algebraic variety equipped with an algebraic symplectic form. This article of PTVV is the first of a series of articles they are writing on the deformation quantization (after Kontsevich) of derived stacks. We will discuss their example of the shifted symplectic structure on BG where G is an algebraic group. We will also talk about their theorem that the fiber product "or intersection" of two Lagrangians in a shifted symplectic space (derived stack) itself carries a shifted symplectic structure. If time permits, we will discuss some local structure theorems (or Darboux Theorems) of Joyce, Brav, Bussi et. al which can be found at http://arxiv.org/abs/1305.6302 http://arxiv.org/abs/1312.0090 and an interesting structure on multiple fiber products: http://arxiv.org/abs/1309.0596. These projects fit into an overall program of Joyce which can be found at http://people.maths.ox.ac.uk/joyce/PGhandout.pdf