We present a detailed analysis of the white dwarf luminosity functions derived from the local 40 pc sample and the deep proper motion catalog of Munn et al. (2014, 2017). Many of the previous studies ignored the contribution of thick disk white dwarfs to the Galactic disk luminosity function, which results in an erronous age measurement. We demonstrate that the ratio of thick/thin disk white dwarfs is roughly 20% in the local sample. Simultaneously fitting for both disk components, we derive ages of 6.8-7.0 Gyr for the thin disk and 8.7 ± 0.1 Gyr for the thick disk from the local 40 pc sample. Similarly, we derive ages of 7.4-8.2 Gyr for the thin disk and 9.5-9.9 Gyr for the thick disk from the deep proper motion catalog, which shows no evidence of a deviation from a constant star formation rate in the past 2.5 Gyr. We constrain the time difference between the onset of star formation in the thin disk and the thick disk to be 1.6 +0.3−0.4 Gyr. The faint end of the luminosity function for the halo white dwarfs is less constrained, resulting in an age estimate of 12.5 +1.4−3.4 Gyr for the Galactic inner halo. This is the first time ages for all three major components of the Galaxy are obtained from a sample of field white dwarfs that is large enough to contain significant numbers of disk and halo objects. The resultant ages agree reasonably well with the age estimates for the oldest open and globular clusters.