DGGS Professional Report 125, 40Ar/39Ar and U-Pb geochronology of Cretaceous-Paleocene igneous rocks and Cenozoic strata of northwestern Cook Inlet, Alaska: Linkages between arc magmatism, cooling, faulting, and forearc subsidence, presents results from 53 40Ar/39Ar and 51 U-Pb analyses of 73 sedimentary, intrusive, and volcanic rock samples collected in the south-central Tyonek Quadrangle of southern Alaska. These data provide new age control and provenance information for igneous and sedimentary rock units throughout the study area--some of which lack prior geochronologic age assignments. The samples were collected in concert with new geologic mapping of approximately 900 square miles encompassing parts of the Late Cretaceous-Paleogene magmatic arc and Cenozoic forearc basin in south-central Alaska. Detailed stratigraphic studies of the entire Cenozoic succession were undertaken at the same time. The widespread exposures of forearc strata in the map area are surface correlatives to hydrocarbon-hosting and commercially producing units in the adjacent subsurface of Cook Inlet basin to the southeast. The results inform structural and depositional models for the Cook Inlet forearc basin that are leveraged to assess tectonic events affecting the continental margin. Intrusive crystallization dates and geochemistry of igneous rocks define episodes of arc magmatism in the region at ca. 84-78 Ma, ca. 74-71 Ma, ca. 69-65 Ma, and ca. 62-57 Ma. Mafic and intermediate volcanics with arc to intra-plate signatures are restricted to a period of reduced arc magmatism from about 57 to 47 Ma. Bedrock cooling from approximately 550 degrees C to below 150 degrees C occurred monotonically, but at varying rates. The cooling trends are consistent with thermal conduction after shallow melt emplacement followed by structurally controlled cooling during the early Paleocene. New dates of reworked tephras from Cenozoic forearc strata constrain the depositional age of the West Foreland Formation at a maximum of ca. 47 Ma to ca. 38 Ma. The dates bracket renewed arc volcanism and middle Eocene syntectonic sedimentation at the western basin margin. More sparsely dated Tyonek and Beluga formations produced zircon U- Pb maximum depositional dates of ca. 15.3-15.2 Ma, and ca. 11.2-9.7 Ma, respectively. These dates are used to anchor a large existing palynologic dataset from the area. New and previously published palynologic results indicate that the oldest Hemlock Conglomerate extends to middle Eocene and thus is partially contemporaneous with West Foreland deposition. Sediment accumulation rates calculated from dated stratigraphic intervals and revised stratigraphic age ranges of the West Foreland Formation and Hemlock Conglomerate suggest a pronounced decrease in basin subsidence during Hemlock deposition followed by an order of magnitude increase in sediment accumulation rates by the middle Miocene. Conglomerate clast dates and detrital grains from reworked tephras provide additional insights into sediment provenance that help refine a depositional model for the Paleogene basin margin. The results highlight the transition from high-gradient, small-catchment alluvial systems sourced from the structurally exhumed arc to a mature, trunk fluvial network distributing a mixed sediment load from proximal arc and distal basement sources during a period of low basin accommodation. Dextral faults extending for nearly 250 km from the upper Cook Inlet to the Matanuska Valley constituted a linked structural system from late Paleocene to middle Eocene that created transtensional depocenters at major fault step-overs along the northwestern and northern margins of the forearc basin. Orogen-parallel extension of the arc region directly to the north is a mechanical consequence of an eastward increase in strike-slip displacement along the fault system. The resulting normal faults produced conduits for magmas sourced from a depleted mantle reservoir during a lull in arc magmatism, and likely facilitated subsidence in the Susitna successor basin. Paleocene to Eocene initiation of dextral strike-slip faults and extension of the arc region supports models for Paleogene oroclinal bending of Alaska. All files are available from the DGGS website: http://doi.org/10.14509/30554.