# Reference on complex cobordism

I am trying to study a little of algebraic cobordism and I lack background from the classic setting. Hence, I am looking for a textbook or expository writing covering the basics of complex cobordism.

Do you know any suitable reference for the basics of complex cobordism?

If possible, I would like the reference to cover a particular result. Let $$E$$ be a spectrum representing a cohomology theory and $$MU$$ the spectrum representing complex cobordism. As an analogy with the algebraic case, it should hold that $$E^*(MU)\simeq E^*(pt)[[c_1,c_2, \ldots]]$$ where $$c_i$$ are the universal Chern classes. In other words, $$E^*(MU)\simeq E^*(Gr)$$ where $$Gr$$ denotes the infinite Grassmanian. If possible, I would like the reference to cover such result and its surroundings.

In particular the result you want is true only for complex orientable cohomology theories (those theories for which we can define $$c_1$$). This is to be expected, since what you want is essentially a version of the Thom isomorphism, that should hold only if the vector bundle is orientable for your cohomology theory.
Also, Adams works on homology rather than cohomology (it is a lot more convenient when having non-finite spaces like $$BU_n$$), but of course once you've proven you have a Thom class, the Thom isomorphism theorem holds in cohomology as well, thus proving the statement you're after.