Nirvana, made up of guitarist and vocalist Kurt Cobain, bassist Krist Novoselic, and drummer Dave Grohl (the fifth and final to fill the position), were an American grunge band and one of the most influential bands of the 1990s. Cobain died in his home on April 5, 1994 and was not discovered until three days later by his electrician. Like Muse, Nirvana was a band comprised of three people who began playing as teens.
The members of Muse have cited Nirvana and the rest of the grunge scene as a major early influence on their music, and Muse's earliest demos have elements similar to Nirvana's music.
Nirvana's second album, Nevermind, is one of Wolstenholme's favourite albums, while Dominic Howard prefers their final, In Utero. Howard has said that Nirvana "influenced practically everyone at some point".
In their earliest days Muse covered Nirvana's song Tourette's in a local Battle of the Bands.
During the Resistance Tour the band commonly played the riff to School, a song on Nirvana's debut album Bleach, as an outro, usually to either New Born or Stockholm Syndrome. Another riff they commonly play after "Stockholm Syndrome" is from Endless, Nameless, the hidden track on Nevermind. At the Reading Festival in 2017, Matt briefly played the riff to "Breed" but not in its entirety as an outro.
Chris in an interview for Radioundercover:
We were into Nirvana when we were younger, when we were in previous bands we did covers of their stuff, it was what got us into bands really, it was what made us want to be in bands.
A video of Muse playing the riffs from "School" and "Endless, Nameless" live can be seen here 
Both living former members of Nirvana, Krist Novoselic and Dave Grohl, have met Muse. Novoselic appeared on the back-stage guest-list for a 2004 Muse show; Grohl, as the Foo Fighters frontman, has played on a number of festivals with Muse. It is known that Grohl is quite a fan of Muse, especially for their live shows.