THE initial motivation of this paper comes from a result of Segre [ 121 about the real lines on a real cubic surface. As it is well known a smooth complex cubic surface has exactly 27 (complex) lines. In the real case this is not always true anymore. A smooth real cubic surface can have 27,15,7 or 3 real lines. This has been well known since the 19th century. The result of Segre we are alluding to is far less known and introduces a more subtle difference between the real and complex cases. Segre distinguishes two types of real straight lines (see below Section 6 for precise definitions) and shows that on a real cubic surface with 27 real lines 15 are of one type and 12 of the other (in fact the result is more complete and gives the classification in all cases-see Theorem 6.2 below). Segre proved this result by studying the degeneration of non-singular cubic surfaces to the union of 3 planes and a special “graphical” way of representing the occurring situations. Noting that the basic difference between the two types of lines is that their respective tubular neighbourhoods in the surface differ by a full twist in P3, our initial aim was to give a new interpretation and a new proof of this result in terms of the Pinstructure induced by the embedding of the surface in P3 (p3 taken with a fixed Spin structure). More precisely, we will show that the two type of lines distinguished by Segre are also differentiated at the homology level by the mod4 quadratic form canonically associated with the above Pinstructure. A further point of interest is that, assuming that the complexification X(C) c p’(C) of the surface X is also non-singular and that the surface is an M-surface, there is another Pinstructure, induced by the embedding of X(R) in X(@) (see [6]). This second form differs from the first by a “privileged” class in H’ (X, Z/2), a class which seems to deserve further investigations. We will explicitly compute this class for quadric and cubic surfaces. The work done for surfaces in P3 led us to study more generally immersions of surfaces in arbitrary orientable 3-manifolds. Using the theory of Spin and Pinstructures (see, for example, [lo] and the book [6]), we consider the problem of associating, as above, quadratic forms with immersions of surfaces in 3-manifolds. We have done this by reformulating results of Pinkall [ 111, where only the case of Iw3 is considered and results of Hass and Hughes [S] where the immersions of surfaces into arbitrary 3-manifolds is studied, but not in terms of quadratic forms. Following Pinkall we will also introduce the notion of immersed surfaces (an equivalence class of immersions-see Sections 4 and 10) and study the relationships between different equivalence relations on immersed surfaces (regular homotoppy, cobordism, equivalence of the Pinstructures) extending the results Pinkall