I'm amazed that there hasn't been a reasonable length write-up on this subject yet, so I'm going to give it a go. Please bear in mind that I am very far from being an expert in this area of music... Please /msg me with any additions or corrections, or write a better write-up yourself...
Country music or Country And Western (C&W) started as a label used for music made by rural white Americans, usually from the Southern USA. Musically this style, at least at the start, was almost indistinguishable from the blues - there is very little to distinguish Jimmie Rodgers and Robert Johnson in my mind other than popularity and colour.
The first major country star was Jimmie Rodgers, 'the singing brakeman'. His distinctive keening style, incorporating yodeling, was the epitome of what was then called 'hilbilly music'. A truly great singer-songwriter, his Blue Yodel #9, featuring Louis Armstrong, was a truly groundbreaking performance, uncategorisable as country, jazz or blues.
Many great records were also put out prewar by The Carter Family, who continued for many decades under the leadership of Maybelle Carter with various daughters taking the place of deceased elders. June Carter (a second generation member) later married Johnny Cash. Their daughter Roseanne Cash is now also a country musician.
Two new forms of country music developed in the late 30s and early 40s. Bluegrass, epitomised by Bill Monroe, was a 'rootsy' form, mostly played on guitar, banjo and fiddle, characterised by incredibly fast picking and high two part harmonies. Western Swing meanwhile, whose chief exponents were Bob Wills and the Texas Playboys, was a poppier form, heavily influenced by the swing music of the day. Western Swing was viewed with suspicion by purists at the time, to the extent that when Hank Williams used a drummer (a Western Swing innovation as far as country goes) at the Grand Ole Opry (country's premier radio show) and as late as 1951 the drummer had to use just one snare, and hide behind a curtain.
Hank Williams was responsible for more country standards than almost anyone else - Hey, Good Lookin', Cold, Cold Heart, Your Cheatin' Heart, Jambalaya, You Win Again, I'm So Lonesome I Could Cry and more than I can name were his work, two minute masterpieces of heartbreak, or genuinely funny novelty songs, Hank was probably the inventor of rock 'n' roll, though his tragically early death prevented him from seeing this.
As the 50s progressed it became increasingly hard to tell country from rock 'n' roll. Elvis Presley performed at the Louisiana Hayride and Grand Ole Opry, and the B-side of his first single was Bill Monroe's Blue Moon Of Kentucky. Chuck Berry's Maybelline was based on the Western Swing song Ida Mae (aka Ida Red), the Everly Brothers owed an obvious debt to bluegrass predecessors such as the Louvin Brothers, Bill Haley And The Comets were originally a western swing band called Bill Haley And His Saddlemen, and so on...
Gradually one form of music, that part of rock 'n' roll which most obviously owed its roots to Hank Williams, became classed instead as rockabilly. Early Elvis, Gene Vincent, Jerry Lee Lewis, Johnny Cash, Carl Perkins and almost any white man who ever recorded for Sun Records qualify for this genre. Often based on simple rhythms, with Cash's boom-chick-a-boom guitar/boogie bassline formula being typical, this music more than any other is what influenced modern country.
There have been many great country artists post-1955 or so, but I simply don't know enough to set them in historical context, so I will simply provide a list of some, and hope someone else can help fill in the details.:
More to be added as they occur to me...
Tlachtga is right of course - but those spirituals were descended from Scottish hymns anyway, and there was a lot of intermixing between the white and black forms of music. Both blues and country had, particularly in the 20s and 30s, an emphasis on guitar, similar chord structures (12-bars etc), and used variations on a pentatonic scale incorporating 'blue notes'.