We explain that general differential calculus and Lie theory have a common
foundation: Lie Calculus is differential calculus, seen from the point of view
of Lie theory, by making use of the groupoid concept as link between them.
Higher order theory naturally involves higher algebra (n-fold
groupoids).(conceptual, topological) differential calculus, groupoids, higher
algebra($n$-fold groupoids), Lie group, Lie groupoid, tangent groupoid, cubes
of ringsComment: V2 : minor corrections; to appear in: Proceedings of 50. Seminar
  Sophus Lie, Banach Center Publications, Warsa