# On the Lie and Cartan Theory of Invariant Differential Systems, III

## TL;DR

This paper discusses the transition from infinitesimal to finite invariant differential systems, emphasizing the simplicity of infinitesimal calculations in Lie and Cartan theory.

## Contribution

It provides an analysis of the infinitesimal aspects of invariant differential systems and outlines the transition to finite systems, building on previous parts.

## Key findings

- Simplifies calculations on the infinitesimal level
- Highlights the transition from infinitesimal to finite systems
- Provides a framework for understanding invariant differential systems

## Abstract

It is presently our aim to undertake the discussion, of the Parts I and II, on the infinitesimal level and outline as well the transition from infinitesimal to finite, the main reason for this being, of course, the well known fact that arguments and calculation on the infinitesimal level are far simpler that those on the finite level.