"Proofs and Fundamentals: A First Course in Abstract Mathematics" is a textbook designed as a transition course for students to introduce them to the creation of rigorous mathematical proofs and fundamental mathematical concepts such as sets, functions, relations, and cardinality. The second edition of this work serves as a bridge between computational courses like calculus and theoretical, proof-oriented courses such as linear algebra, abstract algebra, and real analysis. The book is divided into three parts: the first part covers logic and basic proof techniques, the second part addresses fundamental materials, while the third part introduces a variety of additional topics such as groups, combinatorics, and sequences. The writing style is friendly and encouraging, focusing on informal discussions without neglecting the high standards regarding rigor and writing quality.