English Translation of "Über Graphen und ihre Anwendung auf Determinantentheorie und Mengenlehre" by Dénes Kőnig

The presented work focuses on problems from determinant theory, set theory and topology. The term graph is the binding element that connects these problems. Graphs are distinguished by their geometrical simplicity, which helps in showing the equivalence between various seemingly unrelated problems, besides providing solutions to several open questions discussed here.