This paper presents a quantitative analysis of stream systems and their drainage basins, focusing on the hydrophysical principles governing their development. The author introduces several key concepts, including stream orders, drainage density, bifurcation ratio, and stream-length ratio, which allow for the quantitative description of drainage systems. Stream orders are defined such that the first-order streams are unbranched, second-order streams receive only first-order tributaries, and so on. Drainage density, defined as the total length of streams per unit area, is a critical factor in characterizing the development of a drainage basin. The paper also discusses the laws of stream numbers and lengths, which are based on geometric series. The law of stream numbers states that the number of streams of a given order follows an inverse geometric series, while the law of stream lengths states that the average length of streams of a given order follows a direct geometric series. These laws extend Playfair's law, which describes the "nice adjustment" of stream and valley junctions, and provide a quantitative interpretation of it. The infiltration theory of surface runoff is introduced, which considers the maximum rate at which soil can absorb rain and the functional relationship between surface detention and runoff. The critical length of overland flow, $ x_e $, is the minimum length required to initiate erosion. The erosive force and erosion rate are directly proportional to runoff intensity, distance from the watershed, and other factors. The paper also discusses the development of rill channels and the process of cross-grading, which leads to the formation of new stream systems. The paper concludes that the geometric-series laws of stream numbers and lengths are fully explained by the processes of erosion and cross-grading. A belt of no erosion exists around the margin of each drainage basin, and the development of interior divides is a result of competitive erosion. The final form of a drainage basin is often ovoid or pear-shaped, with the end point of stream development occurring when no overland flow exceeds the critical length. The paper also discusses the relationship between stream development and valley development, emphasizing their close connection and mutual influence. The final surface of a drainage basin is described as a "graded" surface, distinct from a peneplain. The hydrophysical concepts applied to stream and valley development account for observed phenomena from the time of terrain exposure, and these phenomena may be modified by geological structures and subsequent changes. The paper also considers the Davis erosion cycle, which is usually assumed to begin after the development of at least a partial stream system, and the hydrophysical concept, which carries stream development back to the original newly exposed surface.This paper presents a quantitative analysis of stream systems and their drainage basins, focusing on the hydrophysical principles governing their development. The author introduces several key concepts, including stream orders, drainage density, bifurcation ratio, and stream-length ratio, which allow for the quantitative description of drainage systems. Stream orders are defined such that the first-order streams are unbranched, second-order streams receive only first-order tributaries, and so on. Drainage density, defined as the total length of streams per unit area, is a critical factor in characterizing the development of a drainage basin. The paper also discusses the laws of stream numbers and lengths, which are based on geometric series. The law of stream numbers states that the number of streams of a given order follows an inverse geometric series, while the law of stream lengths states that the average length of streams of a given order follows a direct geometric series. These laws extend Playfair's law, which describes the "nice adjustment" of stream and valley junctions, and provide a quantitative interpretation of it. The infiltration theory of surface runoff is introduced, which considers the maximum rate at which soil can absorb rain and the functional relationship between surface detention and runoff. The critical length of overland flow, $ x_e $, is the minimum length required to initiate erosion. The erosive force and erosion rate are directly proportional to runoff intensity, distance from the watershed, and other factors. The paper also discusses the development of rill channels and the process of cross-grading, which leads to the formation of new stream systems. The paper concludes that the geometric-series laws of stream numbers and lengths are fully explained by the processes of erosion and cross-grading. A belt of no erosion exists around the margin of each drainage basin, and the development of interior divides is a result of competitive erosion. The final form of a drainage basin is often ovoid or pear-shaped, with the end point of stream development occurring when no overland flow exceeds the critical length. The paper also discusses the relationship between stream development and valley development, emphasizing their close connection and mutual influence. The final surface of a drainage basin is described as a "graded" surface, distinct from a peneplain. The hydrophysical concepts applied to stream and valley development account for observed phenomena from the time of terrain exposure, and these phenomena may be modified by geological structures and subsequent changes. The paper also considers the Davis erosion cycle, which is usually assumed to begin after the development of at least a partial stream system, and the hydrophysical concept, which carries stream development back to the original newly exposed surface.