I'd recommend by starting with the talk by Daniel Marshall (one of the authors) from Lambda Days 2023, "A Hitchhiker's Guide to Linearity", https://www.youtube.com/watch?v=QtlkqJGdnuM
The latter tutorial is based on "Quantitative program reasoning with graded modal types" (ICFP 2019), with the talk and paper available at https://dl.acm.org/doi/10.1145/3341714
The Granule Project's website, https://granule-project.github.io/, links relevant resources, too, in particular https://granule-project.github.io/granule.html and https://github.com/granule-project/granule/blob/main/example...
The latter tutorial is based on "Quantitative program reasoning with graded modal types" (ICFP 2019), with the talk and paper available at https://dl.acm.org/doi/10.1145/3341714
See also "Linearity and Uniqueness: An Entente Cordiale" (ESOP 2022), https://granule-project.github.io/papers/esop22-paper.pdf