The SMART-s (Spectral Measurements for Atmospheric Radiative Transfer—spectroradiometer) acquires Sun/sky observations for retrieving optimal information on trace gases and aerosols with minimal assumptions. Overall, the algorithm of SMART-s incorporates a series of retrievals, from fundamental quantities (i.e., column abundance of trace gases and aerosol loading) to higher-order geophysical parameters (e.g., aerosol physicochemical properties and vertical profiles), utilizing Sun/sky spectral radiance measurements. This paper describes the theoretical basis for column retrievals of trace gases and aerosols. Associated profile retrievals will be presented in follow-up papers. The current algorithm retrieves the fine/coarse mode of the particle size distribution and spectral complex index of refraction and, thereby, the spectral aerosol single-scattering albedo ω0. SMART-s retrieval is unique particularly in its high spectral resolution of the complex index of refraction and ω0 from near-ultraviolet to near-infrared wavelengths, which is pivotal information for atmospheric chemistry, climate and other inversions. We theoretically assessed information content and retrieval accuracy of the algorithm and compared different type of measurements including the Aerosol Robotic Network (AERONET) and standard Pandora. For the same levels of radiometric accuracy, SMART-s measurements provide the most informative aerosol retrievals based on theoretical error analyses. Higher spectral resolution measurements are particularly beneficial for particle size distribution and fine-mode refractive index retrievals. We applied this algorithm to the AERONET Sun/sky measurements at Kanpur, India, in 2016 to assess algorithm consistency. Even with different assumptions and numerical methods for the inversion, SMART-s retrieved aerosol parameters agreed well with the AERONET operational products (e.g., absolute mean bias errors less than 0.01 for ω0).