Edward Witten's paper explores the relationship between $D$-brane charges and K-theory, a branch of algebraic topology. The author argues that $D$-brane charges take values in the K-theory of spacetime, a concept that has been suspected before. The paper provides new insights into recent proposals, such as the Type I zerobrane, and introduces new objects like a $-1$-brane in Type I superstring theory. The introduction highlights the importance of understanding $D$-brane charges in terms of K-theory rather than cohomology, supported by various arguments, including the propagation of gauge fields on $D$-brane worldvolumes and the dependence of $D$-brane charges on the geometry of submanifolds and gauge fields. The paper also discusses the treatment of $D$-branes on orbifolds and the appearance of Bott periodicity in the brane spectrum of different string theories. The main body of the paper is organized into several sections. Section two poses and answers questions about Type I superstring theory, providing intuitive answers that will be revisited in the context of K-theory. Section three explains the basic relation between the brane-antibrane system and K-theory, while section four completes the identification of $D$-brane charges with K-theory using Sen's description of brane-antibrane bound states and the Thom isomorphism or Bott class. Section five generalizes the discussion to orbifolds and orientifolds, including the Neveu-Schwarz three-form field $H$. Section six discusses worldsheet constructions for special cases, including the Type I zerobrane and a new Type I $-1$-brane. The paper concludes by emphasizing the significance of K-theory in understanding nonperturbative behavior in string theory and the insights it provides into the nature of $D$-brane charges.Edward Witten's paper explores the relationship between $D$-brane charges and K-theory, a branch of algebraic topology. The author argues that $D$-brane charges take values in the K-theory of spacetime, a concept that has been suspected before. The paper provides new insights into recent proposals, such as the Type I zerobrane, and introduces new objects like a $-1$-brane in Type I superstring theory. The introduction highlights the importance of understanding $D$-brane charges in terms of K-theory rather than cohomology, supported by various arguments, including the propagation of gauge fields on $D$-brane worldvolumes and the dependence of $D$-brane charges on the geometry of submanifolds and gauge fields. The paper also discusses the treatment of $D$-branes on orbifolds and the appearance of Bott periodicity in the brane spectrum of different string theories. The main body of the paper is organized into several sections. Section two poses and answers questions about Type I superstring theory, providing intuitive answers that will be revisited in the context of K-theory. Section three explains the basic relation between the brane-antibrane system and K-theory, while section four completes the identification of $D$-brane charges with K-theory using Sen's description of brane-antibrane bound states and the Thom isomorphism or Bott class. Section five generalizes the discussion to orbifolds and orientifolds, including the Neveu-Schwarz three-form field $H$. Section six discusses worldsheet constructions for special cases, including the Type I zerobrane and a new Type I $-1$-brane. The paper concludes by emphasizing the significance of K-theory in understanding nonperturbative behavior in string theory and the insights it provides into the nature of $D$-brane charges.