2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67093Together with F. Morel, we have constructed in \cite{CR, Cobord1, Cobord2} a theory of {\em algebraic cobordism}, an algebro-geometric version of the topological theory of complex cobordism. In this paper, we give a survey of the construction and main results of this theory; in the final section, we propose a candidate for a theory of higher algebraic cobordism, which hopefully agrees with the cohomology theory represented by the $¶^1$-spectrum $MGL$ in the Morel-Voevodsky stable homotopy category.K-Theory and Homology19E15, 14C99, 14C25text