I teach a gemara shiur to older folks, with a focus on skill-building (understanding the structure and logic behind the gemara).
I find that sometimes -- to give a little peek at how the Torah is so much deeper than we realize, and also for a little variety -- it's been helpful to drop in a little bit of concepts from chassidus and kabbalah that may be hinted at in the text.
For example, mentioning that the Arba Avos Nezikin (four main categories of damage) correspond to four character defects, which are rooted in the four elements.
Or explaining, just as the Avos (Patriarchs) represented different middos (character traits), so too, the Tanaim and Amoriam (sages in the Mishna and Talmud). This explains, for example, why Beis Hillel is always lenient (they're Chessed, "Kindness," which is expansion) and why Beis Shammai is always strict (they're Gevurah, "Strength/Justice," which is constriction.)
I've picked up a few concepts over the years, but not a whole lot. Do you know of any Jewish books that systematically go through the Gemara with commentary of this nature?
(I'm looking for something that sheds a different light on the HALACHIC parts of the gemara, NOT for aggada.)