In the first part of my talk I will discuss the notion of 
relativity principle, kinematic algebras, the classification of Leblond and Bacry I will define
the Carroll group and its extensions. I will gave Applications to very 
special Relativity String theory and the BMS algebras. In the second part I will discuss  
plane gravitational waves and how the a subgroup of the  Carroll group acts and how this can be used  
illuminate the currently fashionable topics of gravitational memory and soft 
gravitons. The talk is aimed at a general  audience with a  background in 
Mathematical Physics.