Abstract
This work will deal with important results in Singulariry Theory: the Morse Lemma, as well as, Morse lemma with parameters. For this purpose, we will study: the differential geometry to the plane curves and space curves, the smooth maps from $\mathbb{R}^n$ to$\mathbb{R}$, the right equivalence, jets, regular values and tangent spaces. Besides, we will examine some examples.