A group of mostly French mathematicians which began meeting in the 1930s, aiming to write a thorough unified account of all mathematics. They had tremendous influence on the way math is done since. For a very accessible sampler see Dieudonne Mathematics: The Music Of Reason (Orig. Pour L'honneur De L'esprit Humain).
The founding is described in Andre Weil's autobiography, titled something like ``memoir of an apprenticeship" (orig. Souvenirs D'apprentissage). There is a usable book Bourbaki by J. Fang. Liliane Beaulieu has a book forthcoming, which you can sample in ``A Parisian Cafe and Ten Proto-Bourbaki Meetings 1934-1935" in the Mathematical Intelligencer 15 no.1 (1993) 27-35.
The history behind Bourbaki is also described in Scientific American, May 1957.