Introduction to Geometric Measure Theory(Chap 1-5)

I made this note when reading this textbook. This subject is not very attractive to me so I merely finished half of the book(Chap 1-5).

Covering:
   1. Preliminary measure theory: Hausdorff measure, density, comparison theorems and differentiation theorems
  2. Preliminary geometry and analysis: Lipschitz function and BV function, compactness theorem, first/second variation of submanifold, area/coarea formula
  3. Countably n-rectifiable sets: approximation tangent space, structure theorem, reduced boundary of locally finite perimeter set
  4. Rectifiable n-varifold: variation, stationary monotonicity formula, general monotonicity formula(L^p generalized mean curvature)
  5. Allard regularity theorem: Lipschitz and harmonic approximation, regularity theorem(rectifiable varifold is locally the graph of a C^{1,1-n/p} function).