There are bands that shuffle humbly onto the stage of Madison Square Garden, happy to be there and nervous about filling the room with sound. (And with fans.) Then there is Muse.

Muse, a famously bombastic trio from Britain, is now established as one of the biggest bands in Europe. American fans are coming around too: “Black Holes and Revelations” (Warner Brothers), the most recent Muse album, has sold about 350,000 copies in the United States. So Monday’s concert at the Garden made sense: It was an impressive, cheerfully overblown performance by a band that has never pretended to think small.

The set began with a whooshing ride through “Knights of Cydonia,” in which a long overture gives way to Matthew Bellamy’s crooned invitation: “Come ride with me through the veins of history.” In Muse’s world, this counts as idle banter.

Mr. Bellamy’s voice is often compared to the operatic moan of Thom Yorke, from Radiohead, although Mr. Yorke might beg to differ. At times, Muse sounds like what Radiohead has strenuously avoided becoming: a theatrical arena-rock juggernaut, unafraid of ridiculous lyrics or huge space-age riffs.