This chapter yields a gentle introduction to one-parameter real Lie groups of transformations. In fact, in Mathematical Physics, Lie groups often emerge as transformations. The main properties of Lie groups of transformations are discussed, also by means of some examples. Then, the infinitesimal version of Lie groups of transformations is introduced, and Lie first fundamental theorem proved. The definitions of invariant functions and invariant surfaces, as well as the associated theorems, giving necessary and sufficient conditions, are exploited. Moreover, the canonical variables associated to a one-parameter Lie group of transformations are detailed. Multi-parameter Lie groups of point transformations are described, together with the three Lie fundamental theorems. The link between the infinitesimal version of an r-parameter Lie groups and an r-dimensional Lie algebra is established.