2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153464We construct an invariant of 3-manifolds using a modification of the Kontsevich integral and Kirby's calculus. This invariant, as expected in perturbative Chern-Simon theory, takes values in the algebra of oriented 3-valent graphs. This algebra is a Hopf algebra, graded by half the number of vertices in 3-valent graphs. The degree 1 term of the invariant coincides with Casson-Walker-Lescop invariant. The degree $n$ term is constructed out of the universal Vassiliev invariant of links of degree less than or equal to $(l+1)n$ where $l$ is the number of link components.33 pages, Ams-LaTex, a ready postcript file of the paper is available at http://www.math.buffalo.edu/~letu/Quantum Algebratext