The practical use of Lie symmetries can be quite limited when analyzing differential equations arising in concrete applications on the basis of phenomenological reasoning. In fact, the terms involved in a differential equation can be of different orders of magnitude, and some may be multiplied by very small coefficients. In such cases, the presence of small terms determines the loss of many symmetries. These equations can be studied by suitably defining an approximate Lie theory. This chapter presents a recently introduced approach to approximate Lie groups of differential equations that is consistent with the principles of perturbative analysis. In particular, after introducing approximate Lie groups of point transformations and building their prolongations, the condition for the approximate invariance of differential equations is stated. For ordinary differential equations containing small terms, the approximate symmetries allow for their order reduction, whereas, in the case of partial differential equations, it is possible to obtain approximate invariant solutions. Moreover, the approach is used for searching approximate variational symmetries of Lagrangians containing small terms, and stating an approximate Noether theorem.