The depletion in both the most volatile and most refractory rare earth elements (REEs) in meteoritic refractory inclusions known as group II calcium-, aluminum-rich inclusions (CAIs), was originally thought to be a direct manifestation of high-temperature (over 1700 K) solar nebula condensation. In this scenario, the fractionation in REE abundances arose from: (1) partial equilibrium condensation and removal of the most refractory REEs in ultrarefractory grains prior to CAI formation; (2) complete condensation of the moderately refractory REEs in CAIs; and (3) incomplete condensation of the most volatile REEs (Eu and Yb) that remained in the gas until after CAIs formed. The stable isotopic compositions of 8 REEs (Ce, Nd, Sm, Eu, Gd, Dy, Er, Yb) in 8 CAIs (7 with highly fractionated group II REE abundance patterns) are measured to unravel the evaporation/condensation processes that those CAIs experienced. Contrary to expectation for the equilibrium condensation scenario outlined above, significant light isotope enrichment has been found for the most refractory REEs and more subdued isotopic variations for the less refractory REEs. This suggests that group II CAIs formed by a two-stage process involving fast evaporation of pre-existing materials, followed by near-equilibrium recondensation. The astrophysical context where this could have happened is uncertain, but could have involved episodic intense heating in one or several energetic events akin to EX Lupi type outbursts of eruptive pre-main-sequence stars. In Chapter 2, I introduce the principle of the double-spike (DS) technique and discuss the correction of DS in the presence of isotopic anomalies. In Chapter 3, Analytical methods for REE isotope analyses are discussed. A series of geostandards were measured using DS technique to define the REE isotopic compositions of the bulk silicate Earth. In Chapter 4, the range of equilibrium isotopic fractionation of Eu and Dy in nature is estimated using the synchrotron technique of nuclear resonance inelastic X-ray scattering (NRIXS) and Ab initio calculations. The equilibrium fractionation factors of Eu and Dy are extrapolated to all REEs to estimate the range of REE equilibrium isotopic fractionation in nature including the nebular condition. In Chapter 5, REE isotopic compositions in 8 CAIs are reported. The REE isotopic fractionations are discussed. The timescale of the event responsible for the CAI formation is estimated based on modeling.