This chapter deals with Lie groups of point transformations leaving ordinary differential equations invariant. It is shown how the order of an ordinary differential equation can be algorithmically lowered by using an admitted Lie symmetry. The process is illustrated both using canonical variables and differential invariants. For first-order ordinary differential equations it is also shown how to construct a first integral. Moreover, multiple order reductions are possible provided that the admitted symmetries we use span a solvable Lie algebra. The classification of canonical second-order ordinary differential equations reducible to quadrature is presented, and the form of a general second-order equation that can be mapped to \(u^{\prime \prime }=0\) is characterized. Finally, the method for deriving first integrals of a higher order equation is discussed. Several examples are given to illustrate the theoretical methods.