So this is a highly personal list of history and theory works that have informed my teaching and historical practice. I rarely teach these texts directly, but I often teach the concepts embedded in them.
The Social Construction Texts.
There are five of these that are really important to me, all of which I read in my first three years in grad school. First was Barbara Jean Fields' Slavery Race and Ideology in the United States of America and the related Ideology and Race in American History. These two important articles helped establish the idea of the social construction of race in the US (although books like Degler's Neither Black nor White, and Gossett's Race the History of an Idea laid important groundwork towards that). One of the money quotes is here at the end of Ideology and Race "
Race is neither the reflex of primordial attitudes nor a tragically recurring central theme. It became the ideological medium through which Americans confronted questions of sovereignty and power because the enslavement of Africans and their descendants constituted a massive exception to the rules of sovereignty and power that were increasingly taken for granted. And, despite the changes it has undergone along the way, race has remained a predominant ideological medium because the mannerof slavery's unraveling had lasting consequences for the relations of whites to other whites, no less than for those of whites to blacks.
Two other important works were on gender. Judith Butler's Gender Trouble and Joan Scott's Gender: A Useful Category of Historical Analysis. The latter pointed out that gender is relational. The former is a real tough read. So, I'll summarize. Gender is performative. It is not the parts or the plumbing (that's sex). It is both the ideas we have about the correct or appropriate ways of behaving for boys and girls, men and women, and the ways those ideas are put into practice via laws and customs and the ways they are enforced and resisted. Gender is what turns a classroom of girls into preps, and hos, and jockettes.
Now when you combine race and gender you get Chela Sandoval's idea about the differential mode of consciousness as a strategy of resistance. There's a couple of variations of this argument that Sandoval has made over the years, but it really doesn't matter which one you get your hands on. Here's the most important take away: identity for women of color operates like the clutch of an automobile. Depending on context, women will engage whatever identity or identities seem most likely to produce the best result in context (this has been hipped up to be called code switching). They might express their solidarity with white women one hour, and later, emphasize a shared blackness (or Mexicanness or whatever). Although Sandoval was writing about women of color, I found something similar going on with men in my own dissertation and the notion of situational identity was profoundly lifechanging for me as a historian, a teacher, and in my day-to-day interactions.
The Space and Place Texts
A second set of influential texts came from Geography. David Harvey's The Condition of Postmodernity is probably still a must read for understanding the conditions of what he optimistically calls late capitalism. (I much preferred Harvey to Jameson's Postmodernism.) Whether you agree with Harvey's politics, the argument he makes about the differences between Modernism and Postmodernism (including a handy little chart in the back) are very useful. I also found his Justice, Nature and the Geography of Difference to be very helpful for thinking through issues of space, place, and time. But it's poorly edited and a bit of a rush job. Keith Basso's Wisdom Sits in Places is my other go to book on geography. Basso shows how the Western Apache use storytelling to turn spaces into meaningful places. Profoundly important for my own work on contested landscapes and something that's easily conveyed to students.
Texts by French Guys and Anthropologists. Not necessarily in that order.
A third set of influential texts are classics in the Critical Theory genre. First, the Americans. Clifford Geertz on Balinese cockfight. If you haven't read this, go read it right now. It single handedly created what we call The Cultural Turn in history. Barbara Babcock's notion that "what is socially marginal is often symbolically central" is pretty important here too, although I just spared you having to read anywhere that it came from. I use this in class all the time. Then there's James Clifford's Identity in Mashpee article which shows how identity and legal forms collided incoherently.
So confession time, I haven't read a lot of Foucault. But by the time I hit grad school a lot of Foucault had already been incorporated into history practice. So I just skimmed a couple of texts (Discipline and Punish, the stuff on the panopticon) and thought "what's the big deal?" Far more important to me are two other texts. First there is Michel de Certeau's The Practice of Everyday Life. de Certeau argued that despite modern life's tendency to try to regiment and regulate humanity, individuals found creative ways to resist such regimentation. After I read this, I paid far more attention to the dynamics of everyday interactions (can you see how this connects to Geertz?). I started looking at patterns of movement and everyday economic and social exchanges and examining them for their multiple meanings. In my own dissertation, it led to the insight that although roads were paved on the Navajo reservation to reach uranium, the same roads led to Navajos traveling to towns much more often. Many of these insights were extended by radical anthropologist James C. Scott. His magnificent Seeing Like a State points out the difference between learned or practical knowledge gained through experience and generalized knowledge. Scott points out how "certain schemes to improve the human condition fail". It's a great book, and it will help you understand your department chair and division head better.
Another key text by a Frenchman is Bordieu's Distinction. I don't really follow his argument strictly. But the basic idea, that cultural performances (of race, gender, etc.) tie to class structures is an important one. I pay a lot of attention to this in my teaching. If we think about things like the rituals of party politics in antebellum America, Bordieu's insights become valuable.
So that's the intellectual framework, I'm working from. I'm sure there are things I'm missing here. (Michael Taussig, Evelyn Brooks Higginbotham, Edward Hall, and Walter Benjamin jump to mind, maybe I'll do a part 2 later).
And as always, the single person who shaped me intellectually was my dissertation adviser, Susan Lee Johnson, who introduced me to most of these texts. You should go read her award-winning book Roaring Camp.