The paper presents the optical and near-infrared (NIR) luminosity and stellar mass functions of galaxies in the local Universe, using data from the Two Micron All Sky Survey (2MASS) and the Sloan Digital Sky Survey (SDSS). The authors estimate corrections for passband shifting and galaxy evolution, and present-day stellar mass-to-light (M/L) ratios by fitting optical-NIR galaxy data with simple models. The optical and NIR luminosity functions constructed agree with recent literature determinations within uncertainties. The authors argue that 2MASS is biased against low surface brightness galaxies and use SDSS data and stellar population knowledge to estimate the 'true' K-band luminosity function, which has a steeper faint end slope and higher luminosity density than the direct estimate. Assuming a universal stellar initial mass function (IMF), the authors find good agreement between the stellar mass function derived from 2MASS/SDSS data and that of Cole et al. (2001). The stellar mass function has a steeper faint end slope than -1.1, reflecting the low M/L ratios of low-mass galaxies. The authors estimate an upper limit to the stellar mass density in the local Universe as Ω* h = 2.0 ± 0.6 × 10⁻³, assuming an IMF rich in low-mass stars. The stellar mass density may be lower if a different IMF is assumed. The authors examine type-dependence in the optical and NIR luminosity functions and the stellar mass function, finding that early-type galaxies have larger characteristic luminosity or mass than later types, and the faint end slope is steeper for later types. Accounting for typing uncertainties, the authors estimate that at least half, and possibly up to three-quarters, of the stellar mass in the Universe is in early-type galaxies. The paper also presents the relationship between model stellar M/L ratios and colors in SDSS/2MASS passbands, an updated discussion of near-infrared stellar M/L ratio estimates, and the volume-corrected distribution of g and K-band stellar M/L ratios as a function of stellar mass. The authors discuss the data, data quality, and selection effects, including magnitude accuracy, concentration parameters, and completeness. They also discuss the methodology for deriving k-corrections, evolution corrections, and stellar M/L ratios, and construct and discuss optical and NIR luminosity functions for their galaxy sample. They construct stellar mass functions and discuss them further, and summarize their results. The paper is arranged with sections on data, methodology, luminosity functions, stellar mass functions, and a summary. The authors also discuss systematic uncertainties, including those from galaxy age, dust, and bursts of star formation. The paper concludes with the luminosity functions and their implications for galaxy evolution.The paper presents the optical and near-infrared (NIR) luminosity and stellar mass functions of galaxies in the local Universe, using data from the Two Micron All Sky Survey (2MASS) and the Sloan Digital Sky Survey (SDSS). The authors estimate corrections for passband shifting and galaxy evolution, and present-day stellar mass-to-light (M/L) ratios by fitting optical-NIR galaxy data with simple models. The optical and NIR luminosity functions constructed agree with recent literature determinations within uncertainties. The authors argue that 2MASS is biased against low surface brightness galaxies and use SDSS data and stellar population knowledge to estimate the 'true' K-band luminosity function, which has a steeper faint end slope and higher luminosity density than the direct estimate. Assuming a universal stellar initial mass function (IMF), the authors find good agreement between the stellar mass function derived from 2MASS/SDSS data and that of Cole et al. (2001). The stellar mass function has a steeper faint end slope than -1.1, reflecting the low M/L ratios of low-mass galaxies. The authors estimate an upper limit to the stellar mass density in the local Universe as Ω* h = 2.0 ± 0.6 × 10⁻³, assuming an IMF rich in low-mass stars. The stellar mass density may be lower if a different IMF is assumed. The authors examine type-dependence in the optical and NIR luminosity functions and the stellar mass function, finding that early-type galaxies have larger characteristic luminosity or mass than later types, and the faint end slope is steeper for later types. Accounting for typing uncertainties, the authors estimate that at least half, and possibly up to three-quarters, of the stellar mass in the Universe is in early-type galaxies. The paper also presents the relationship between model stellar M/L ratios and colors in SDSS/2MASS passbands, an updated discussion of near-infrared stellar M/L ratio estimates, and the volume-corrected distribution of g and K-band stellar M/L ratios as a function of stellar mass. The authors discuss the data, data quality, and selection effects, including magnitude accuracy, concentration parameters, and completeness. They also discuss the methodology for deriving k-corrections, evolution corrections, and stellar M/L ratios, and construct and discuss optical and NIR luminosity functions for their galaxy sample. They construct stellar mass functions and discuss them further, and summarize their results. The paper is arranged with sections on data, methodology, luminosity functions, stellar mass functions, and a summary. The authors also discuss systematic uncertainties, including those from galaxy age, dust, and bursts of star formation. The paper concludes with the luminosity functions and their implications for galaxy evolution.