"Proofs and Fundamentals: A First Course in Abstract Mathematics" 2nd edition is designed as a transition course to introduce undergraduates to the writing of rigorous mathematical proofs and to fundamental mathematical ideas such as sets, functions, relations, and cardinality. The text serves as a bridge between computational courses like calculus and more theoretical, proofs-oriented courses such as linear algebra, abstract algebra, and real analysis. This three-part work carefully balances proofs, fundamentals, and extras. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material such as sets, functions, and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics, and sequences. A gentle, friendly style is used, where motivation and informal discussion play a key role, while maintaining high standards in rigor.