The main objectives of this chapter are to present, discuss, and classify some elementary types of local bifurcations that occur at fixed points in ordinary differential equations (ODEs). In particular, we will classify the saddle-node, transcritical, and pitchfork bifurcations, the latter unfolding into two cases: (i) supercritical and (ii) subcritical. For each asymptotically stable fixed point, we will present its corresponding basin of attraction.