This book provides an understanding of the classification of D-branes in string theory based on the study of anomalies in the world-sheet theory. Studying D-branes is an important window into the nature of string theory beyond the perturbative formulation. Detailed analysis of D-branes helps us reach an understanding of various string dualities. Although tachyon condensation and K-theory have historically played an essential role in describing D-branes, the constructions and nature of D-branes have recently been revisited from the viewpoint of anomalies in the world-sheet theory. In the last decade, it has been revealed that anomalies in quantum field theory are captured by symmetry-protected topological (SPT) phases on a manifold of one higher dimension through the anomaly inflow mechanism. This formulation of anomalies enables us to compute not only perturbative but also global anomalies. The aim of this book is to present constructions of D-branes, including non-supersymmetric ones, together with their properties, such as K-theoretic classification, along this recent progress in anomalies. This book begins with a review of the world-sheet description of string theory. The author emphasizes the importance of SPT phases and anomalies on the world-sheet. Subsequently, the relation between D-branes and K-theory is reviewed. After reviewing the fundamental material, we explain the construction of D-branes in Type II and Type I superstring theory based on the analysis of the anomalies in the world-sheet with boundaries. In the main part of the book, we discuss D-branes in the Dabholkar-Park (DP) background, which is an orientifold theory in nine-dimensional spacetime. The book clarifies that several properties of D-branes in the DP background can be deduced from the careful analysis of anomalies.