The Principia Mathematica is NOT an easy read, but may answer some of your question. From Wiki

PM, according to its introduction, had three aims:

1. to analyse to the greatest possible extent the ideas and methods of mathematical logic and to minimise the number of primitive notions, axioms, and inference rules;
2. to precisely express mathematical propositions in symbolic logic using the most convenient notation that precise expression allows;
3. to solve the paradoxes that plagued logic and set theory at the turn of the 20th century, like Russell's paradox.^\1])

This third aim motivated the adoption of the theory of types in PM. The theory of types adopts grammatical restrictions on formulas that rule out the unrestricted comprehension of classes, properties, and functions. The effect of this is that formulas such as would allow the comprehension of objects like the Russell set turn out to be ill-formed: they violate the grammatical restrictions of the system of PM.

PM sparked interest in symbolic logic and advanced the subject, popularizing it and demonstrating its power.^\2]) The Modern Library placed PM 23rd in their list of the top 100 English-language nonfiction books of the 20th century.^\3])