The aim of the book is to study a certain class of curves: Magnetic curves, curves of constant-ratio, etc., or one could focus on some properties of curves. In addition, one can study for example factorable surfaces, affine factorable surfaces, factorable surfaces with density. In a study of these surfaces for example, the focus can lie on the curvatures, log-linear density. It is known that many physical processes can be formulated in the form of curves or surfaces so this thesis is interested in studying some special curves and surfaces in the Euclidean and pseudo-Euclidean spaces and then studying their geometric properties.