Chapter 1. Introduction ......................................1 §1. Outline .................................................1 §2. Mathematical notations ...................................2 §3. Absence of energy and momentum density ..................2 §4. Center-of-mass moment ...................................4 Chapter 2. General Lagrangian formulation ....................7 §1. δL .....................................................7 §2. H= ZμHμ+ dB ...........................................9 §3. Hμ is proportional to variational derivatives ..........10 §4. The role of B ..........................................11 §5. δH ...................................................12 Chapter 3. Lagrangian formulation in GR .....................16 §1. Various theories in relativity .........................16 §2. L EC in GR ..............................................18 §3. δL EC ..................................................20 §4. H and B ................................................22 §5. δH and C ..............................................23 §6. H vs. δH and B vs. C ..................................26 §7. ∫Σ H= -NP+ (1/2)λJ ..................................28 §8. Covariant Differentials ................................30 Chapter 4. Application in the Linearized theory of gravity ..34 §1. Introduction ...........................................34 §2. Basic quantities in weak- field limit ..................34 §3. Orders of magnitude ....................................40 §4. Quasilocal Quantities in Weak Fields ...................41 Chapter 5. Evaluation of the COM moment .....................44 §1. First- order expansion of quantities; Connections ......44 i. Metrics ...............................................44 ii. Metric Densities ......................................45 iii. △η, etc. ............................................46 iv. Connections ...........................................46 v. Expansion of N and DN .................................48 §2. Various B forms ........................................48 i. The Komar- type expressions ...........................49 ii. The Freud- type expressions ...........................50 §3. Evaluation of the conserved quantities .................51 i. P0 ....................................................52 ii. Pj’s and Jjk’s ........................................58 iii. J0j’s: the COM moments ................................58 Chapter 6. Conclusion and Discussion ........................65 References ..................................................68