American Woman's release date is listed as simply "January 1970" -- no specific date, but I'm making it my 1970 Album of the Week for the end of January / beginning of February.
The band already had a history before releasing American Woman, -- they started out in 1958 as Allan and the Silvertones, then became Chad Allan and the Reflections in 1962, then Chad Allan and the Expressions in 1965.
Their 1965 cover of Johnny Kidd and the Pirates' "Shakin' All Over" was released with a marketing gimmick: It was credited to "Guess Who?" in hopes that people would think it was an uncredited recording by the Beatles or another British Invasion band. DJs continued crediting it to "Guess Who?" even after the Expressions were revealed as the band, so they changed their name, then dropped the question mark in 1968.
They broke out for real in 1970 with American Woman's title track, their only number one single in the United States and the first Canadian single to top the US Hot 100.
And the album was, IMO, their high point -- Randy Bachman performed his last show with them that May, then returned to Canada to form what later became Bachman-Turner Overdrive. It was, once again IMO, all downhill from there for The Guess Who.
The album may have been the high point for the band, but I don't consider the title track to be the high point of the album. Here's my favorite cut -- "No Sugar Tonight / New Mother Nature":