Introduction to graded bundles
  We review the concept of a graded bundle as a natural generalisation of a vector bundle. Such geometries are particularly nice examples of more general graded manifolds. With hindsight there are many examples of graded bundles that appear in the existing literature. We start with a discussion of graded spaces, passing through graded bundles and their linearisation to end with weighted (graded) Lie groupoids/algebroids. 
Andrew J. Bruce, K. Grabowska, J. Grabowski
math.DG math-ph math.MP