group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
A line bundle is a vector bundle of rank (or dimension) $1$, i.e. a vector bundle whose typical fiber is a $1$-dimensional vector space (a line).
For complex vector bundles, complex line bundles are canonically associated bundles of circle group-principal bundles.
The class of line bundles has a nicer behaviour (in some ways) than the class of vector bundles in general. In particular, the dual? of a line bundle $L$ is a weak inverse of $L$ under the tensor product of line bundles. Thus the isomorphism classes of line bundles form a group.
Over any manifold there is canonically the density line bundle which is the associated bundle to the principal bundle underlying the tangent bundle by the determinant homomorphism.