These are my solutions to the problems in The Geometry of Physics by Theodore Frankel. Writing solutions here encourages me to present them in a clear and understandable way.
Ch. 1. Manifolds and Vector Fields.
Ch. 2. Tensors and Exterior Forms.
2.1 Covectors and Riemannian Metrics
2.3 The Cotangent Bundle and Phase Space
2.5 The Grassmann or Exterior Algebra
2.6 Exterior Differentiation
2.8 Orientation and Pseudoforms
2.9 Interior Products and Vector Spaces