Something mutual is held in common or experienced between two parties, as in mutual friends. Similarly, reciprocal indicates a balanced relationship between two or more people, in which an act, thing, or feeling is given in return for another. Unlike mutual, reciprocal also carries the meaning of “matching or equivalent.” So a reciprocal promise may be made to ensure that both parties will maintain confidentiality about a matter. Often used in math, navigation, and grammar, reciprocal has a more technical implication of being one-for-one or the exact opposite or inverse of something, whereas mutual features in the world of finance or insurance when assets are shared (e.g., mutual funds). 

There are many types of knowledge, and erudition is one of them. Erudition is a thorough, formal, and profound sort of knowledge obtained by extensive research. The term is often used to discuss knowledge in fields other than those of mathematics and the physical sciences—so you're more likely to encounter it in discussion of philosophy or literature than in discussion of biology. Erudition is not a high-frequency word in English, but when it is used, it's likely to be in a context of glowing appreciation, as something that inspires respect or awe.

Interesting is one of those familiar adjectives that we reach for so often, it verges on filler. Compelling is a more intense form of interesting that can bring your meaning into focus. When something is compelling, in the sense of having a powerful and irresistible effect, it commands our attention. The adjective comes from the verb compel, which means "to force or drive, especially to a course of action." Compelling cases or compelling arguments force us to consider them. Art can be visually compelling, drawing us in and capturing our attention. Similarly, good books are often described as compelling if we cannot put them down.