This paper presents a two-dimensional (2-D) fitting algorithm, GALFIT (Version 3), which allows for the study of structural components of galaxies and other astronomical objects in digital images. The algorithm improves upon previous 2-D fitting methods by enabling the use of irregular, curved, logarithmic, and power-law spirals, rings, and truncated shapes within traditional parametric functions like Sérsic, Moffat, King, and Ferrer profiles. These new features allow for the creation of realistic galaxy model images by mixing and matching shape features, applying them to multiple model components, and maintaining the intuitive meaning of key parameters like the Sérsic index and effective radius. The algorithm has potential applications in quantifying galaxy asymmetry, low surface brightness tidal features, and decomposing galaxy subcomponents in the presence of strong rings and spiral arms. The paper illustrates these features through case studies showing various levels of complexity. The paper discusses the challenges of analyzing astronomical images due to the diversity of object sizes and shapes, particularly for galaxies. Parametric fitting, which models galaxy light distribution using analytic functions, has been the mainstay of galaxy imaging studies. This technique was first applied by de Vaucouleurs (1948) and later expanded by Freeman (1970) to study galaxy structure and evolution. Parametric fitting has been used in many applications, including the study of disk galaxies, the Tully-Fisher relation, galaxy evolution, and the fundamental plane of spheroids. The paper also discusses non-parametric analysis, which does not involve deciding on a functional form or number of parameters. Non-parametric techniques, such as decomposing images into shapelets or wavelets, are useful for quantifying galaxy mergers and measuring concentration and asymmetry. However, these techniques often do not account for image smearing by the PSF and different sensitivity thresholds between surveys. The paper presents the GALFIT algorithm, which is a 2-D parametric galaxy fitting algorithm that allows for complex image decomposition tasks. It uses the Levenberg-Marquardt technique to find the optimum solution to a fit and calculates the goodness of fit using the reduced chi-squared statistic. The algorithm accounts for image smearing by the PSF and allows for the use of a PSF image. It also considers the effects of telescope optics and atmospheric seeing on image quality. The paper discusses the concept of a model component, which is defined by the surface brightness profile. Each model component can take on a shape that is completely unrecognizable from a traditional ellipsoid shape. The radial profile functions describe the intensity fall-off of a model away from the peak, such as the Sérsic, Nuker, or exponential models. The paper also discusses the azimuthal shape functions, which generate the projected shape in the x-y plane of the image. These functions include generalized ellipses, Fourier modes, bending modes, and coordinate rotation functions. The paper concludes with a discussionThis paper presents a two-dimensional (2-D) fitting algorithm, GALFIT (Version 3), which allows for the study of structural components of galaxies and other astronomical objects in digital images. The algorithm improves upon previous 2-D fitting methods by enabling the use of irregular, curved, logarithmic, and power-law spirals, rings, and truncated shapes within traditional parametric functions like Sérsic, Moffat, King, and Ferrer profiles. These new features allow for the creation of realistic galaxy model images by mixing and matching shape features, applying them to multiple model components, and maintaining the intuitive meaning of key parameters like the Sérsic index and effective radius. The algorithm has potential applications in quantifying galaxy asymmetry, low surface brightness tidal features, and decomposing galaxy subcomponents in the presence of strong rings and spiral arms. The paper illustrates these features through case studies showing various levels of complexity. The paper discusses the challenges of analyzing astronomical images due to the diversity of object sizes and shapes, particularly for galaxies. Parametric fitting, which models galaxy light distribution using analytic functions, has been the mainstay of galaxy imaging studies. This technique was first applied by de Vaucouleurs (1948) and later expanded by Freeman (1970) to study galaxy structure and evolution. Parametric fitting has been used in many applications, including the study of disk galaxies, the Tully-Fisher relation, galaxy evolution, and the fundamental plane of spheroids. The paper also discusses non-parametric analysis, which does not involve deciding on a functional form or number of parameters. Non-parametric techniques, such as decomposing images into shapelets or wavelets, are useful for quantifying galaxy mergers and measuring concentration and asymmetry. However, these techniques often do not account for image smearing by the PSF and different sensitivity thresholds between surveys. The paper presents the GALFIT algorithm, which is a 2-D parametric galaxy fitting algorithm that allows for complex image decomposition tasks. It uses the Levenberg-Marquardt technique to find the optimum solution to a fit and calculates the goodness of fit using the reduced chi-squared statistic. The algorithm accounts for image smearing by the PSF and allows for the use of a PSF image. It also considers the effects of telescope optics and atmospheric seeing on image quality. The paper discusses the concept of a model component, which is defined by the surface brightness profile. Each model component can take on a shape that is completely unrecognizable from a traditional ellipsoid shape. The radial profile functions describe the intensity fall-off of a model away from the peak, such as the Sérsic, Nuker, or exponential models. The paper also discusses the azimuthal shape functions, which generate the projected shape in the x-y plane of the image. These functions include generalized ellipses, Fourier modes, bending modes, and coordinate rotation functions. The paper concludes with a discussion