Professor Marc Levine Mathematics, Northeastern University Complex cobordism is an example of an extraordinary cohomology theory. It is in fact the universal "complex oriented" theory. Quillen made clear the deeper meaning of this property by relating complex cobordism to the theory of formal group laws. There is now a version of cobordism in the setting of algebraic varieties, called algebraic cobordism (constructed by Levine and Morel). This has the analogous universal property and relation to formal group laws as complex cobordism. We give an introduction to this theory, describe its relation with the theory of algebraic cycles as well as algebraic vector bundles and coherent sheaves, give applications to Riemann-Roch theorems and show how to construct Adams operations.