Not being very familiar with the Ukrainian Cossacks, I choose to research this topic, supposing others in the class might also be unfamiliar. A great source, of course, is the Encyclopedia of Ukraine article at
The Cossacks began as free soldiers, protecting the steppe area from Turkish and Tartar raids. Although it does not seem clear to me, it appears their founding was even supported or allowed by the Polish-Lithuanian powers to assist in protecting the area. As the Cossacks grew in numbers and power, the Polish-Lithuanian Commonwealth first tried to regulate them, and then later gave the them limited autonomy while still under Polish-Lithuanian control. By the late 1500s, the Cossacks began making their own external treaties but still assisted the Polish Army in certain battles: 1618, Moscow and 1621, Khotyn.
Of particular note is the Cossack-Polish Ward, 1648 to 1657. In some regards, this war is hailed as a great event--a Cossack uprising gathering a large portion of the Ukrainian populace and yielding a Cossack state. However, this state was never able to gain complete autonomy, the result of the war seeming to remove them from Polish rule, only to place them under Russian rule. Also, the local people fared very poorly, with all armies being very cruel and murdering many people (women, children, clergymen, Jews, etc.) of the opposing side.
This Cossack state mentioned above existed from 1648 until 1782. Although initially the general populous had more freedom under this state, soon class hierarchies again controlled available freedoms. The state was abolished by Catherine II in 1764--the governing bodies replaced by Russian organizations and serfdom for the peasants. Only few of the ruling Cossacks were given Russian nobility status. During the 1800s, army regiments were sometimes formed from previous Cossack groups, and periodic Cossack protests were engaged, resulting in the social class remaining somewhat distinct.
As a last note, an anti-socialist Ukrainian government formed in 1918, called the Hetman government, certainly with ties to the historical Cossacks. However, it was too closely tied with Czarist Russia, and after the Bolshevik revolution, the Hetman government eventually surrendered powers to the socialist Ukrainian National Republic in December 1918.
This is just a very brief historical outline of the Cossacks, but I think it adds some interesting perspective to some of our class discussion regarding Schevchencko, Cossacks and Ukrainian Nationalism.