I would like to begin my first exploration of the arts of differential geometry/topology with the first volume of M. Spivak's five-volume set in the different geometry. Is a thorough understanding of vector calculus must before reading his book? I read neither of his Calculus nor Calculus on Manifolds, but I just begun to read Loomis/Sternberg (quite exciting) and Hubbard/Hubbard. Unfortunately, my knowledge of vector calculus is quite shaky (only knows the definitions of topics like directional derivative and line integrals). Please let me know if Spivak's first volume builds directly upon his "Calculus on Manifolds". If the prerequisite of vector calculus is not strictly necessary, I would like to begin reading the first volume as I like to learn nonlinearly. I am also currently reading Spanier's Algebraic Topology and Lang's Algebra. I acquired the topological background from Singer/Thorpe and Engelking.