An outline of polar spaces: basics and advances

This paper is an extended version of a series of lectures on polar spaces given during the workshop and conference \lq Groups and Geometries\rq\, held at the Indian Statistical Institute in Bangalore in December 2012. We firstly give a concise exposition of the theory of polar spaces, ending up with the classification of polar spaces of rank at least $3$. Then we present a few related research topics, as polar spaces of infinite rank, non-linear embeddings of polar spaces, projective embeddings of dual polar spaces and polar grassmannians.