Q: I would like to know more about the animal offerings. I know that each animal refers to an aspect within us. What do they mean with respect to our inner emotions or thoughts?
A: As Rashi explains, in general, the bull or cow corresponds to Abraham, and the attribute of lovingkindness.
The goat corresponds to Yitzchak, and the attribute of awe and strength.
The sheep corresponds to Jacob, and the attribute of beauty and mercy.
In addition, the bull represents the rectification of the (attacking) bull in one's soul, the negative trait of over-aggression.
The goat represents the rectification of brazenness, the negative trait of chutzpah.
The sheep represents the rectification of unchecked desire, the negative trait of permissiveness.