2.1 Definition of a linear vector space
  2.1.1 Problems
 2.2 Linear independence and basis vectors
  2.2.1 The scalar product
  2.2.2 Questions
 2.3 Function spaces
  2.3.1 Continuous basis functions: Fourier Transforms
  2.3.2 General orthogonality and completeness in function spaces
  2.3.3 Example from Quantum Mechanics
 2.4 Appendix