Topics on algebraic cobordism

We will discuss some topics on the theory of algebraic cobordism. These include the computation via envelopes and the descent exact sequence. We review the relation of algebraic cobordism with Chow and $K$-theory. We will also discuss an extension of the cobordism rings of smooth varieties to the singular setting via a well-behaved operational bivariant theory. As an example, we describe the operational equivariant cobordism of toric varieties.