Curvature Of The Lower Bound Of Alexandrov Space

This paper is based on parts of the report in the seminar of Alexandrov space in the fall semester of 2007 at Capital Normal University given by Prof.Rong and the paper "An introduction to the geometry of Alexandrov space" written by Shiohama.First of all,we collect the definitions of curvature bounded below and prove that these definitions are equivalent for locally compact intrinsic space.Here a new proof is given for Alexandrov lemma.Secondly,we give some examples of the Alexandrov space with curvature bounded below and compute the geodesic and the curvature of them.In the last section,we discuss the Globalization theorem by using the idea given in[BGP]in details.