Algebraic Topology I
  
Notes 
    
  1. Introduction and homotopy and CW complexe
    1. CW complexe
    2. Homotopy
  2. The fundamental group and covering spaces
    1. The funamental group
    2. Simple computations
    3. Fundamental gropu of S^1
    1. Van Kampen's Theorem
    1. Covering spaces
  3. Homology Theory
    1. Singular Homology
    2. Introduction to homological algebra (maps on homology)
    3. Relative homology and excision
    4. Degree and cellular homology
    5. Homology with different coeficient 
    1. Formalism
    2. Geometric interpretation of homology 
  4. Cohomology
    1. Cohomology of a chain complex 
    2. Cohomology of a space
    3. Product
    4. More products
  5. Poincare Duality
    1. Statement and consequences
    2. Fundamental classes of manifolds
    3. Algebraic limits and the proof of duality
    4. Next steps in algebraic topology