In this talk, we will introduce some results on multiplicative differential geometry of singular curves and surfaces in multiplicative Euclidean space. These include multiplicative evolute, multiplicative parallels, multiplicative evolutoids, multiplicative pedaloids and multiplicative primitivoids of multiplicative plane curve, as well as multiplicative spherical Darboux image and multiplicative rectifying developable surface. Then we also generalize multiplicative evolutoids and multiplicative pedaloids to the category of multiplicative frontal curves. In addition, we obtain the classification theorem of singularities in multiplicative space and establish the relationships between singularities of some objects and multiplicative geometric invariants. Finally, we will present theoretical results through a series of illustrative examples. This is a joint work with Jiaxin Li, Xinyu Yao and Zikun Ma.