Rotation curves of spiral galaxies are essential for understanding their mass distribution, dynamics, and evolution. They are derived from observations of emission and absorption lines in the spectra of galaxies, providing insights into the velocity of gas and stars within the galaxy. These curves reveal the distribution of mass, including dark matter, and help determine the rotational behavior of galaxies. The study of rotation curves has evolved significantly since the early 20th century, with early observations by Slipher and Pease, and later advancements in technology enabling more precise measurements. Rotation curves typically show a flat or slowly rising profile, which contradicts the expected Keplerian decline and suggests the presence of dark matter. The flatness of rotation curves in many spiral galaxies has led to the conclusion that dark matter dominates the mass distribution. The analysis of rotation curves involves various methods, including intensity-weighted velocities, centroid velocities, and envelope tracing, each with its own advantages and limitations. High-resolution observations, such as those using CO and HI lines, have provided detailed insights into the structure and dynamics of spiral galaxies. These observations have revealed the presence of massive black holes at the centers of some galaxies, as well as the effects of nuclear warps, counterrotation, and resonance rings on the kinematics of galaxies. The study of rotation curves in different environments, such as galaxy clusters, has shown that environmental factors can influence the kinematics of galaxies, leading to disturbed rotation curves. The statistical properties of rotation curves indicate that the shape and amplitude of rotation curves vary with galaxy luminosity, morphology, and environment. The universal rotation curve, which is a function of total luminosity and radius, has been proposed as a general model for spiral galaxies. However, exceptions exist, particularly in galaxies with disturbed kinematics or in clusters where environmental effects are significant. The analysis of rotation curves continues to be a vital tool in astrophysics, providing critical information about the mass distribution, dynamics, and evolution of spiral galaxies. Advances in observational techniques and computational methods are expected to further refine our understanding of these complex systems.Rotation curves of spiral galaxies are essential for understanding their mass distribution, dynamics, and evolution. They are derived from observations of emission and absorption lines in the spectra of galaxies, providing insights into the velocity of gas and stars within the galaxy. These curves reveal the distribution of mass, including dark matter, and help determine the rotational behavior of galaxies. The study of rotation curves has evolved significantly since the early 20th century, with early observations by Slipher and Pease, and later advancements in technology enabling more precise measurements. Rotation curves typically show a flat or slowly rising profile, which contradicts the expected Keplerian decline and suggests the presence of dark matter. The flatness of rotation curves in many spiral galaxies has led to the conclusion that dark matter dominates the mass distribution. The analysis of rotation curves involves various methods, including intensity-weighted velocities, centroid velocities, and envelope tracing, each with its own advantages and limitations. High-resolution observations, such as those using CO and HI lines, have provided detailed insights into the structure and dynamics of spiral galaxies. These observations have revealed the presence of massive black holes at the centers of some galaxies, as well as the effects of nuclear warps, counterrotation, and resonance rings on the kinematics of galaxies. The study of rotation curves in different environments, such as galaxy clusters, has shown that environmental factors can influence the kinematics of galaxies, leading to disturbed rotation curves. The statistical properties of rotation curves indicate that the shape and amplitude of rotation curves vary with galaxy luminosity, morphology, and environment. The universal rotation curve, which is a function of total luminosity and radius, has been proposed as a general model for spiral galaxies. However, exceptions exist, particularly in galaxies with disturbed kinematics or in clusters where environmental effects are significant. The analysis of rotation curves continues to be a vital tool in astrophysics, providing critical information about the mass distribution, dynamics, and evolution of spiral galaxies. Advances in observational techniques and computational methods are expected to further refine our understanding of these complex systems.