Can someone tell me the origins of modern Jazz

Jazz started in New Orleans in Congo Square, which was one of the only places in the Americas where slaves were allowed to gather for dances and play their native music.

In the early 1900s, Ragtime piano was combined with those Congo Square rhythms and gospel and field work music to form the rudiments of Jazz.

During World War I, this music was spread all over Europe by American GI's and combined with marching band instruments. Those GI's came home and started using those "jazz" rhythms and incorporating them into Showtune songs (most famously "I've Got Rhythm").

However, the fledgling record industry was still wary about selling this "African" music to the public, so they created two different types of "Jazz" records, black and white. Black labels, like Okeh Records, were sold as "Jazz", a slang term for sex ("Jazzing" someone meant screwing them) as the rhythms and dancing were reminiscent of sex. These records are what most of us consider "Dixieland" Jazz today, featuring up and comers like The Red Hot Peppers and Louis Armstrong. The white records utilized some toned down jazz rhythms in show tunes with mostly white bands.

The 1920's saw Jazz's popularity grow exponentially as it evolved. Louis Armstrong went north to Chicago with King Oliver. Great composers of Jazz like Count Basie and Duke Ellington turned it into an art form. They, along with Crooners like Bing Crosby and Jazz Clarinetist Benny Goodman launched swing in the 1930s, but the Great Depression caused many of the black Jazz clubs to close. This had the unintended consequence of actually putting more of those acts into white clubs and white bands. This brought more and more musicians into contact with one another. They challenged, collaborated, and innovated.

World War 2 sent jazz everywhere from the Pacific to the Baltic. It was no longer just some dance fad in New Orleans, NYC, and Chicago. Post war, the Jazz game changed forever. While crooners ruled the white audiences, black musicians wanted something of their own that white musicians couldn't duplicate. That was Bebop. The rhythms were so complex, the music so technical, that only the most skilled musicians (like Charlie "Yardbird" Parker) could play it. This music was much less accessible and dance-able for mainstream audiences, so it was mostly a more "underground" scene.

In the early 50's, audiences were tiring of crooners and artists were tiring of the complicated, highly technical hard bop. This led to cool jazz with Miles Breakout Album "Birth of the Cool". This cool jazz included South American samba influences. The Modern Jazz Quartet was one of the primary bands leading the movement.

At the same time, artists were going back to their roots. Stride piano, something that had only been used sparingly since 30's swing became popular, was suddenly in vogue. Stripped down call and response with more simple rhythms that one could jam to but were much more energetic than "cool" jazz were what made Hard Bop popular. Hard Bob also received influences from Cuba and France, basically anywhere the mob once operated clubs or American servicemen were once stationed. A perfect example of Hard Bop can be seen in Art Blakey's "Moanin'".
Hard bop (with a stride piano, electric guitar, electric bass, drum set, and horns) was the forerunner to what would later be known as Rock n Roll.