Reb Chaim analyzes a debate between the Rambam and Raavad whether dough which will be split is obligated in Challah, and differentiates between different types of Challah exemption.

Reb Chaim analyzes a ruling of the Rambam as to how a non-Jew's ownership of land in Israel effects the status of the produce (similar to a piece in the Laws of Terumah).

Reb Chaim analyzes a ruling of the Rambam regarding a buyers obligation to bring Bikkurim (first fruits), and explains a core concept in the requirement of ownership for Bikkurim.

Reb Chaim (quoted by his son Reb Velvel) analyzes who owns Maaser Sheini, reinterpreting the Gemara's phrase that it's owned by Hashem, in a conceptually important and fundamental way. 

Reb Chaim analyzes a complex set of cases in the Rambam, yielding insight into the nature of redeeming Maaser Sheini, especially the distinction between redemption and purchasing Maaser Sheini

Reb Chaim analyzes the nature of the exemption of Maaser Sheini (produce which must be eaten in Jerusalem) on produce grown outside of Israel, and contrasts it with the status of a bechor (firstborn animal) born outside of Israel.

Reb Chaim analyzes the obligation of a buyer to take Maaser on produce which was purchased, and reads the Rambam very carefully to uncover a major stringency. 

Reb Chaim analyzes the halacha that non-kosher taste can be diluted and nullified by kosher food, using a case involving terumah as a springboard to analyze the mechanism of nullification (bitul) in halacha. 

Reb Chaim explores the nature of the inheritance of a fetus, using a case in Terumah as a springboard to innovate a new concept of inheritance, somewhat detached from financial ownership.