Formal Geometry of Differential Equations

In this chapter we lay the geometric foundations of the formal theory of differential equations. The name “formal theory” stems from the fact that it is, at least indirectly, concerned with the analysis of formal power series solutions, i. e. one ignores the question whether the series actually converge. Another interpretation of the name is that one tries to extract as much information as possible on the solution space by purely formal operations like algebraic manipulations of the equations or their differentiations without actually solving the given equation.