ABSTRACT We present the volumetric rates and luminosity functions (LFs) of Type Ia supernovae (SNe Ia) from the V-band All-Sky Automated Survey for Supernovae (ASAS-SN) catalogues spanning discovery dates from UTC 2014 January 26 to UTC 2017 December 29. Our standard sample consists of 404 SNe Ia with $m_{\mathrm{{\it V},peak}} \lt 17\, \mathrm{mag}$ and Galactic latitude |b| > 15°. Our results are both statistically more precise and systematically more robust than previous studies due to the large sample size and high spectroscopic completeness. We make completeness corrections based on both the apparent and absolute magnitudes by simulating the detection of SNe Ia in ASAS-SN light curves. We find a total volumetric rate for all subtypes of $R_{\mathrm{tot}} = 2.28^{+0.20}_{-0.20} \times 10^{4}\, \mathrm{yr}^{-1}\, \mathrm{Gpc}^{-3}\, h^{3}_{70}$ for $M_{\mathrm{{\it V},peak}} \lt -16.5\, \mathrm{mag}$ ($R_{\mathrm{tot}} = 1.91^{+0.12}_{-0.12} \times 10^{4}\, \mathrm{yr}^{-1}\, \mathrm{Gpc}^{-3}\, h^{3}_{70}$ for $M_{\mathrm{{\it V},peak}} \lt -17.5\, \mathrm{mag}$) at the median redshift of our sample, zmed = 0.024. This is in agreement (1σ) with the local volumetric rates found by previous studies. We also compile LFs for the entire sample as well as for subtypes of SNe Ia for the first time. The major subtypes with more than one SN include Ia-91bg, Ia-91T, Ia-CSM, and Ia-03fg with total rates of $R_{\mathrm{Ia-91bg}} = 1.4^{+0.5}_{-0.5} \times 10^{3}\, \mathrm{yr}^{-1}\, \mathrm{Gpc}^{-3}\, h^{3}_{70}$, $R_{\mathrm{Ia-91T}} = 8.5^{+1.6}_{-1.7} \times 10^{2}\, \mathrm{yr}^{-1}\, \mathrm{Gpc}^{-3}\, h^{3}_{70}$, $R_{\mathrm{Ia-CSM}} = 10^{+7}_{-7}\, \mathrm{yr}^{-1}\, \mathrm{Gpc}^{-3}\, h^{3}_{70}$, and $R_{\mathrm{Ia-03fg}} = 30^{+20}_{-20}\, \mathrm{yr}^{-1}\, \mathrm{Gpc}^{-3}\, h^{3}_{70}$, respectively. We estimate a mean host extinction of $E(V-r) ≈ 0.2\, \mathrm{mag}$ based on the shift between our V band and the Zwicky Transient Facility r-band LFs.