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1 Cobordism and oriented cohomology 1

1.1 Oriented cohomology theories 1

1.2 Algebraic cobordism 6

1.3 Relations with complex cobordism 13

2 The definition of algebraic cobordism 17

2.1 Oriented Borel-Moore functors 17

2.2 Oriented functors of geometric type 26

2.3 Some elementary properties 29

2.4 The construction of algebraic cobordism 35

2.5 Some computations in algebraic cobordism 40

3 Fundamental properties of algebraic cobordism 51

3.1 Divisor classes 51

3.2 Localization 55

3.3 Transversality 66

3.4 Homotopy invariance 75

3.5 The projective bundle formula 77

3.6 The extended homotopy property 80

4 Algebraic cobordism and the Lazard ring 83

4.1 Weak homology and Chern classes 83

4.2 Algebraic cobordism and K-theory 105

4.3 The cobordism ring of a point 116

4.4 Degree formulas 122

4.5 Comparison with the Chow groups 136

5 Oriented Borel-Moore homology 141

5.1 Oriented Borel-Moore homology theories 141

5.2 Other oriented theories 149