Algebraic topology based on knots may be characterized as a study of 3-manifolds by considering the quotient of the free module generated by links in a manifold by (local) skein relations. Of course, this is not a complete definition of the field, which has itspurely algebraic component (skein algebras of groups), higher manifold generalization and rich internal structure, but at least it gives idea of our subject. In the search for starting point of the theory one should consider the Listing book (1847), the Dedekind and Weber paper (1882), and the Poincar\'e's paper "Analysis situs" (1895). In knot theory, skein modules (building blocks of algebraic topology based on knots) have their origin in an observation by Alexander (1928) that his polynomials of three links $L_+, L_-$ and $L_0$ in $S^3$ are linearly related. This line of research was continued by Conway (linear skein 1969). In the graph theory, the idea of forming a ring of graphs and dividing it by an ideal generated by local relations, was developed by Tutte in his 1946 PhD thesis. The theory of Hecke algebras, as introduced by Iwahori (1964), is closely connected to the theory of skein modules. Another connection can be found in the Temperley-Lieb algebra (1971). The main motivation for skein modules was the discovery/construction of the Jones polynomial (1984). Skein algebras of groups use rich ideas of Poincar\'e (1884) , Vogt (1889), Fricke and Klein (1897) and the school of Magnus (e.g. "Rings of Fricke characters", 1980). Joan Birman introduced me to the world of knots and braids, to the work of her advisor W.Magnus, grand advisor M.Dehn... Her work is continued by her students and grand students (the best recent result related to algebraic topology based on knots was obtained by A.Sikora). I will present the development of the algebraic topology based on knots in the historical context.